Economic-Micro

Economics_Micro_UndergraduateLECTURES3.xlsx

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Production Possibilities

Production Possibilities Curve
Trucks
			Unattainable Without More Resources or Better Technology
		Efficiency
	Inefficiency
				Tanks

Opportunity Cost Example

Production Possibilities for Tom's Factory
			In which of the two goods does Nancy have Comparative Advantage?
			Nancy has comparative advantage in producing cases, because her opportunity cost is lower (.333) whereas Tom's is 3 discs.
Cases			In which of the two goods does Tom have Comparative Advantage?
In Thousands			Tom has comparative advantage in producing Discs because his opportunity cost is lower (.333) whereas Nancy's is 3 Cases
	4
				If Tom and Nancy decide to trade with each other, they can move to this point where they maximize their gains from specialization and trade.
		Nancy's PPF
	1					Red Trade Line
				Tom's PPF
			1			4
					Disks
					In Thousands

Marginal Benefit Curve (Pizza)

Marginal Benefit Curve
Willingness To Pay (CD's Per Pizza)	As the production and availability increases, people consider it less valuable and will pay less
	Shortages create value/Surpluses remove it.
		Pizzas (Production and Availability

Too many Pizzas Produced

Marginal Benefit Curve (CD's)

Marginal Benefit Curve
	CD's (Production and Availability)	As the production and availability increases, people consider it less valuable and will pay less
		Shortages create value/Surpluses remove it.
		Pizzas (Production and Availability)

Too many CD's Produced

Efficient Resources Use Curve

Marginal Benefit Curve
	CD's (Production and Availability)	As the production and availability increases, people consider it less valuable and will pay less
		Shortages create value/Surpluses remove it.
		Pizzas (Production and Availability)

Too many CD's Produced, because value and then price becomes too low

Too many Pizzas Produced, because value and then price becomes too low

Point of Allocative Efficiency Where Both have a maximum value/benefit/price

Circular Flow

Households

Goods and Services

Land, Labor, Capital, Entrepreneurshiip

Goods Markets

Factor Markets

Expenditures on Goods and Services

Wages, Rent, Interest, Profits

Firms

Demand (Individual)

Demand For You And CD's
	Price
	5
	4
	3
	2
	1
									Demand
		1	2	3	4	5	6	7
										Quanity Demanded
	Price	$ 5	$ 4	$ 3	$ 2	$ 1
	Quantity Demanded	1	2	3	4	5

Demand (Individual (2))

Demand For Another And CD's
	Price
	5
	4
	3
	2
	1
									Demand
		1	2	3	4	5	6	7
										Quanity Demanded
	Price	$ 5	$ 4	$ 3	$ 2	$ 1
	Quantity Demanded	1	2	3	4	5

Demand (Total)

Demand For CD Players
	Price
	5
	4
	3
	2
	1
		2000	2200	3	4	5	6	7	8	9	10
										Quanity Demanded
	Price	$ 5	$ 4	$ 3	$ 2	$ 1
	Quantity Demanded	2	4	6	8	10

Demand (Total) (2)

Demand For CD Players
	Price
	150
	125
	100
	75
	50
		1	2	3	4	5	6	7	8	9	10
										Quanity Demanded
	Price	$ 150	$ 125	$ 100	$ 75	$ 50	$ 25
	Quantity Demanded	1	2	3	4	5	6

Supply and Demand (Detail)

Supply and Demand
	Price	a	b	c		Supply
	Surplus
					Equilibrium
	Shortage
						Demand
							Quantity Demanded
							Quantity Supplied

Lower In Taxes and Factor Costs, Better Technology and Expectations, More Subsidies

Increase In Taxes and Factor Costs, Poor Technology and Expectations, Fewer Subsidies

Higher Income, More Buyers, More Liking Product, Other Goods (Substitutes) Available at Higher Price, Lower Cost of Complementary Goods, High Expectations.

Lower Income, Fewer Buyers,Less Liking Product, Other Goods (Substitutes) Available at Lower Price, Increase In Cost of Complementary Goods, Low Expectations.

Demand for Important Products

Demand For Products/Services that Require a Minimum Level of Quality
	Price
		Quantity Demanded

Demand for High Ticket Products

Demand For High-Priced Ticket Items
	Price
		Quantity Demanded

Demand for Prestige Products

Demand For Products/Services thatare Prestigous or with Luxury
	Price
		Quantity Demanded

Supply

Supply For CD's
	Price
	5
	4
	3
	2
	1
		1	2	3	4	5	6	7	8	9	10
										Quanity Supplied
	Price	$ 5	$ 4	$ 3	$ 2	$ 1
	Quantity Supplied	10	8	6	4	2

Elasticity Comparison

Inelastic

Elastic

Price

Okay to raise price

Not good to raise Price

Not good to lower it

Okay to lower it.

Quantity Demanded

A large change in price creates a minimual change in QD

A Small change in price creates a huge change in QD

Should You Change Price (2)

Should You Lower Your Prices To Get More Business?
Scenario 1				Scenario 2
Price	Quantity Demanded	Total Revenue		Price	Quantity Demanded	Total Revenue	Marginal Revenue
$ 100.00	10	$ 1,000.00		$ 8.00	10	$ 80.00
$ 90.00	11	$ 990.00		$ 7.75	11	$ 85.25	$ 5.25
$ 80.00	12	$ 960.00		$ 7.50	12	$ 90.00	$ 4.75
$ 70.00	13	$ 910.00		$ 7.25	13	$ 94.25	$ 4.25
$ 60.00	14	$ 840.00		$ 7.00	14	$ 98.00	$ 3.75
$ 50.00	15	$ 750.00		$ 6.75	15	$ 101.25	$ 3.25
$ 40.00	16	$ 640.00		$ 6.50	16	$ 104.00	$ 2.75
$ 30.00	17	$ 510.00		$ 6.25	17	$ 106.25	$ 2.25
$ 20.00	18	$ 360.00		$ 6.00	18	$ 108.00	$ 1.75
Avg % Ch.	Avg % Ch.			Avg % Ch.	Avg % Ch.
0.105	(0.095)			0.032	(0.095)
(0.905)				(3.000)
Inelastic				Elastic
Scenario 3
Price	Quantity Demanded	Total Revenue	Marginal Revenue	Cost Per Unit	Total Cost	Marginal Cost	Marginal Profit	Total Profit
$ 9.00	1	$ 9.00			$ - 0
$ 8.00	2	$ 16.00	$ 7.00		$ - 0	$ - 0	$ 7.00	$ 7.00	Yes
$ 7.00	3	$ 21.00	$ 5.00		$ - 0	$ - 0	$ 5.00	$ 12.00	Yes
$ 6.00	4	$ 24.00	$ 3.00		$ - 0	$ - 0	$ 3.00	$ 15.00	Yes
$ 5.00	5	$ 25.00	$ 1.00		$ - 0	$ - 0	$ 1.00	$ 16.00	No
$ 4.00	6	$ 24.00	$ (1.00)		$ - 0	$ - 0	$ (1.00)	$ 15.00	No
$ 3.00	7	$ 21.00	$ (3.00)		$ - 0	$ - 0	$ (3.00)	$ 12.00	No
$ 2.00	8	$ 16.00	$ (5.00)		$ - 0	$ - 0	$ (5.00)	$ 7.00	No
$ 1.00	9	$ 9.00	$ (7.00)		$ - 0	$ - 0	$ (7.00)	$ - 0	No

Laffer Curve

	100%
T
A
X
R
A
T
E
	0%
		TAX REVENUE

Higher Taxes Create Lower Revenue As More People Decide to Not Work, Not Work As Much, or Not Report All Income

Elasticity Comparison (2)

Elasticity = Infinite

Elasticity= 0

Elasticity= 1

Perfectly elastic

Perfectly Inelastic

Unit Elastic

Price

Quantity Demanded

Elasticity Template

Ice Cream
Original:	$5.00	Quantity	125
New:	$6.50	Quantity	200
Change:	$1.50	Change:	75
Average:	$5.75	Average:	162.5
% Changes	26.1%		46.2%
			46.2%
			26.1%
	Elasticity:		1.77
The reason that you must find the average price and demand is that change in demand moves both directions.
Need for Refined Formula:
If I start at 2, and have a 50% drop, the QD would be 1
A 50% increase of 1, however does not take you back to 2. The QD would be 1.5 (half again, but not double)
Without using the refined formula, this is how your results would then turn out.
Original Price:	$0.45	Quantity Demanded:	2
New Price:	$0.40	Quantity Demanded:	4
Price Change:	($0.05)	Demand Change:	2
% Changes	-11.1%		100.0%
Price Elasticity of Demand:	(9.00)
Original Price:	$0.40	Quantity Demanded:	4
New Price:	$0.45	Quantity Demanded:	2
Price Change:	$0.05	Demand Change:	(2)
% Changes	12.5%		-50.0%
Price Elasticity of Demand:	(4.00)

Elasticity of Demand (Calc)

Pizza Elasticity of Demand Example				1% Increase In Price	Causes a 1.4% decrease In QD	New Demand
Original Price:	$15.00	Quantity Demanded:	150	$15.15	2.10	147.90
New Price:	$20.00	Quantity Demanded:	100	$15.30	2.07	145.83
Price Change:	$5.00	Demand Change:	-50	$15.45	2.04	143.79
Average Price:	$17.50	Average Demand:	125	$15.61	2.01	141.77
% Changes	28.6%		-40.0%	$15.77	1.98	139.79
			-40.0%
			28.6%
	Price Elasticity of Demand:		1.40
This means that the quantity of pizza demanded will go up 1.4 times as fast by a drop in price of $10
This means that the quantity of pizza demanded will go down 1.4 times as fast by an increase in price of $10
A 1% reduction in the price brings about a 1.4% increase in purchases.
The reason that you must find the average price and demand is that change in demand moves both directions.
Need for Refined Formula:
If I start at 2, and have a 50% drop, the QD would be 1
A 50% increase of 1, however does not take you back to 2. The QD would be 1.5 (half again, but not double)
Without using the refined formula, this is how your results would then turn out.
Original Price:	$0.45	Quantity Demanded:	2
New Price:	$0.40	Quantity Demanded:	4
Price Change:	($0.05)	Demand Change:	2
% Changes	-11.1%		100.0%
Price Elasticity of Demand:	(9.00)
Original Price:	$0.40	Quantity Demanded:	4
New Price:	$0.45	Quantity Demanded:	2
Price Change:	$0.05	Demand Change:	(2)
% Changes	12.5%		-50.0%
Price Elasticity of Demand:	(4.00)

Elasticity of Demand (New Ex)

Price Elasticity of Demand Example				1% Change In Price	Causes a% Change In QD
Original Price:	$50.00	Quantity Demanded:	2800	$50.50	2,722.22	0.0278
New Price:	$75.00	Quantity Demanded:	800	$49.50	2,877.78	0.0278
Price Change:	$25.00	Demand Change:	-2000
Average Price:	$62.50	Average Demand:	1800				Change	New Price	Demand Change In %	From Original	New Demand
% Changes	40.0%		-111.1%				1%	$50.50	-2.78%	(77.78)	2,722.22
Price Elasticity of Demand:	2.78						2%	$51.00	-5.56%	(155.56)	2,644.44
							3%	$51.50	-8.33%	(233.33)	2,566.67
This means that the quantity of pizza demanded will go up 1.22 times as fast by a drop in price of $10							4%	$52.00	-11.11%	(311.11)	2,488.89
This means that the quantity of pizza demanded will go down 1.22 times as fast by an increase in price of $10							5%	$52.50	-13.89%	(388.89)	2,411.11
A 1% reduction in the price brings about a 1.22% increase in purchases.							6%	$53.00	-16.67%	(466.67)	2,333.33
							7%	$53.50	-19.44%	(544.44)	2,255.56
The reason that you must find the average price and demand is that change in demand moves both directions.							8%	$54.00	-22.22%	(622.22)	2,177.78
							9%	$54.50	-25.00%	(700.00)	2,100.00
Need for Refined Formula:							10%	$55.00	-27.78%	(777.78)	2,022.22
If I start at 2, and have a 50% drop, the QD would be 1
A 50% increase of 1, however does not take you back to 2. The QD would be 1.5 (half again, but not double)							-1%	$49.50	2.78%	77.78	2,877.78
							-2%	$49.00	5.56%	155.56	2,955.56
Without using the refined formula, this is how your results would then turn out.							-3%	$48.50	8.33%	233.33	3,033.33
Original Price:	$0.45	Quantity Demanded:	2				-4%	$48.00	11.11%	311.11	3,111.11
New Price:	$0.40	Quantity Demanded:	4				-5%	$47.50	13.89%	388.89	3,188.89
Price Change:	($0.05)	Demand Change:	2				-6%	$47.00	16.67%	466.67	3,266.67
% Changes	-11.1%		100.0%				-7%	$46.50	19.44%	544.44	3,344.44
Price Elasticity of Demand:	(9.00)						-8%	$46.00	22.22%	622.22	3,422.22
							-9%	$45.50	25.00%	700.00	3,500.00
Original Price:	$0.40	Quantity Demanded:	4				-10%	$45.00	27.78%	777.78	3,577.78
New Price:	$0.45	Quantity Demanded:	2
Price Change:	$0.05	Demand Change:	(2)
% Changes	12.5%		-50.0%
Price Elasticity of Demand:	(4.00)

Elasticity of Demand (Rev)

Gasoline Elasticity of Demand Example
Original Price:	$3.07	Quantity Demanded:	5000
New Price:	$3.49	Quantity Demanded:	4500
Price Change:	$0.42	Demand Change:	-500
Average Price:	$3.28	Average Demand:	4750
% Changes	12.8%		-10.5%
Price Elasticity of Demand:	0.82	Relatively Inelastic

Cross Elasticity (Calculations)

YOUR Pizza vs. Burgers Sold Somewhere Else (Substitute Good)
Pizza Price Unchanged
Original Burger Price:	$1.50	Original Quantity Demanded of Your Pizza:	9	Per hour
New Burger Price:	$2.50	New Quantity Demanded of Your Pizza:	11	Per hour
Price Change:	$1.00	Demand Change:	2	Per hour	Change	New Price	Demand Change In %	From Original	New Demand
Average Price:	$2.00	Average Demand:	10		1%	$0.00	-0.20%	- 0	- 0
% Changes	50.0%		20.0%		2%	$0.00	-0.40%	- 0	- 0
Cross Elasticity of Demand:	0.40				3%	$0.00	-0.60%	- 0	- 0
					4%	$0.00	-0.80%	- 0	- 0
This means that the quantity of your pizza demanded will go up .4 times by an increase in the price of a burger of $1					5%	$0.00	-1.00%	- 0	- 0
This means that the quantity of your pizza demanded will go down .4 times by an decrease in the price of a burger of $1					6%	$0.00	-1.20%	- 0	- 0
					7%	$0.00	-1.40%	- 0	- 0
Such a change in price of the burger in this example would shift the demand curve outward.					8%	$0.00	-1.60%	- 0	- 0
Price and the quantity change in demand with substitues are positively correlated.					9%	$0.00	-1.80%	- 0	- 0
					10%	$0.00	-2.00%	- 0	- 0
YOUR Pizza vs. Soft drinks (Complimentary Good).
Pizza Price Unchanged
Original Soft Drink Price:	$1.50	Original Quantity Demanded of Your Pizza:	11	Per hour
New Soft Drink Price:	$3.00	New Quantity Demanded of Your Pizza:	5	Per hour
Price Change:	$1.50	Demand Change:	-6	Per hour
Average Price:	$2.25	Average Demand:	8
% Changes	66.7%		-75.0%
Cross Elasticity of Demand:	1.13
This means that the quantity of your pizza demanded will go down .4 times by an increase in the price of a burger of $1
This means that the quantity of your pizza demanded will go up .4 times by an decrease in the price of a burger of $1
Such a change in price of the burger in this example would shift the demand curve outward.
Price and the quantity change in demand with complements are negatively correlated.

Cross Elasticity (Review)

Subway Subs vs. Arby's
Subway Price unchanged
Original Price Bus :	$3.00	Original Quantity Demanded of Your Subway	1000	Per hour
New Bus Price:	$2.50	New Quantity Demanded of Your Subway:	800	Per hour
Price Change:	($0.50)	Demand Change:	-200	Per hour
Average Price:	$2.75	Average Demand:	900
% Changes	-18.2%		-22.2%
Cross Elasticity of Demand:	1.22
Subway Subs vs. Pepsi
Subway Price unchanged
Original Pepsi Price:	$4.00	Original Quantity Demanded of Your Subs:	450	Per hour
New Pepsi Price:	$3.75	New Quantity Demanded of Your Subs:	600	Per hour
Price Change:	($0.25)	Demand Change:	150	Per hour
Average Price:	$3.875	Average Demand:	525
% Changes	-6.45%		28.6%
Cross Elasticity of Demand:	4.43
Such a change in price of the burger in this example would shift the demand curve outward.
Price and the quantity change in demand with complements are negatively correlated.

Income Elasticity (Calc)

YOUR Wine vs. Income
Wine Price Unchanged
Original Income:	$890.00	Original Quantity Demanded of Your Wine:	45	Per hour
New Income:	$992.00	New Quantity Demanded of Your Wine:	47	Per hour
Income Change:	$102.00	Demand Change:	2	Per hour
Average Income	$941.00	Average Demand:	46
% Changes	10.8%		4.3%
Income Elasticity of Demand:	0.40

Income Elasticity (Review)

YOUR Coca-Cola vs. Income
Your Coca-Cola Price Unchanged
Original Income:	$1,000.00	Original Quantity Demanded of Your Coke:	45	Per hour
New Income:	$900.00	New Quantity Demanded of Your Coke:	40	Per hour
Income Change:	($100.00)	Demand Change:	-5	Per hour
Average Income	$950.00	Average Demand:	42.5
% Changes	-10.5%		-11.8%
Income Elasticity of Demand:	1.12

Should You Change Price

Should You Lower Your Prices To Get More Business?
Scenario 1				Scenario 2
Price	Quantity Demanded	Total Revenue		Price	Quantity Demanded	Total Revenue	Marginal Revenue
$ 100.00	10	$ 1,000.00		$ 8.00	10	$ 80.00
$ 90.00	11	$ 990.00		$ 7.75	11	$ 85.25	$ 5.25
$ 80.00	12	$ 960.00		$ 7.50	12	$ 90.00	$ 4.75
$ 70.00	13	$ 910.00		$ 7.25	13	$ 94.25	$ 4.25
$ 60.00	14	$ 840.00		$ 7.00	14	$ 98.00	$ 3.75
$ 50.00	15	$ 750.00		$ 6.75	15	$ 101.25	$ 3.25
$ 40.00	16	$ 640.00		$ 6.50	16	$ 104.00	$ 2.75
$ 30.00	17	$ 510.00		$ 6.25	17	$ 106.25	$ 2.25
$ 20.00	18	$ 360.00		$ 6.00	18	$ 108.00	$ 1.75
Avg % Ch.	Avg % Ch.			Avg % Ch.	Avg % Ch.
0.105	(0.095)			0.032	(0.095)
(0.905)				(3.000)
Inelastic				Elastic
Scenario 3
Price	Quantity Demanded	Total Revenue	Marginal Revenue	Cost Per Unit	Total Cost	Marginal Cost	Marginal Profit
$ 9.00	1	$ 9.00			$ - 0
$ 8.00	2	$ 16.00	$ 7.00		$ - 0	$ - 0	$ 7.00	Yes
$ 7.00	3	$ 21.00	$ 5.00		$ - 0	$ - 0	$ 5.00	Yes
$ 6.00	4	$ 24.00	$ 3.00		$ - 0	$ - 0	$ 3.00	Yes
$ 5.00	5	$ 25.00	$ 1.00		$ - 0	$ - 0	$ 1.00	No
$ 4.00	6	$ 24.00	$ (1.00)		$ - 0	$ - 0	$ (1.00)	No
$ 3.00	7	$ 21.00	$ (3.00)		$ - 0	$ - 0	$ (3.00)	No
$ 2.00	8	$ 16.00	$ (5.00)		$ - 0	$ - 0	$ (5.00)	No
$ 1.00	9	$ 9.00	$ (7.00)		$ - 0	$ - 0	$ (7.00)	No

Elasticity Comparison (Supply)

Elasticity = Infinite

Elasticity= 0

Elasticity= 1

Perfectly elastic

Perfectly Inelastic

Unit Elastic

Price

Quantity Supplied

Elasticity of Supply (Calc)

Pizza Supply
Original Price:	$10.00	Quantity Supplied	10
New Price:	$12.00	Quantity Supplied	13
Price Change:	$2.00	Supplied Change:	3
Average Price:	$11.00	Average Supply	11.5
% Changes	18.2%		26.1%
Price Elasticity of Supply	1.43

Elasticity of Supply (Review)

DVD Per Night Rental Supply
Original Price:	$5.00	Quantity Supplied	200	Per Night
New Price:	$8.00	Quantity Supplied	230	Per Night
Price Change:	$3.00	Supplied Change:	30
Average Price:	$6.50	Average Supply	215
% Changes	46.2%		14.0%
Price Elasticity of Supply	0.30

Price Ceilings

Supply and Demand
	Price		Supply
		Originally set at equlibrium, caused a shortage when the supply curve shifts.
Rent Ceiling		Equilibrium
			Demand
				Quantity Demanded
				Quantity Supplied

Price Floors

Supply and Demand
	Price		Supply
Minimum wage
		Equilibrium
			Workers not hired due to surplus, causing unemployment and inefficiency.
			Demand
				Quantity Demanded
				Quantity Supplied

Consumption Possibilities

With a Budget of $30 For Only Two Activities										Consumption Possibilities Line
Cost Of A Movie = $6
Cost Of A Six-Pack of Pop = $3
										A
	Movies			Pop			Total	Total Utility (Both)	10
Possibility	Quantity	Total Paid	Total Utility	Quantity	Total Paid	Total Utility	$ Spent
A	0	$0	0	10	$30	291	30	291			B		Unaffordable
B	1	$6	50	8	$24	260	30	310	8
C	2	$12	88	6	$18	225	30	313
D	3	$18	121	4	$12	181	30	302
E	4	$24	150	2	$6	117	30	267	6			C
F	5	$30	175	0	$0	0	30	175
											Affordable
									4				D
				Maximization of Total Utility Within Budget					2					E
				@ 2 Movies and 6 Six-Packs
									0	1	2	3	4	5

Marginal Utility

With a Budget of $30 For Only Two Activities
Cost Of A Movie = $6
Cost Of A ix Pack of Pop = $3
	Movies			Marginal Utility	Pop			Marginal Utility
	Quantity	Total Utility	Marginal Utility	Per Dollar Spent	Quantity	Total Utility	Marginal Utility	Per Dollar Spent
	0	0	0		0	0	0		Buy more Pop at first because they have higher MUPD.
	1	50	50	8.33	1	75	75	25.00 user: I will not use this combo because I have not maximized Marginal Utility
	2	88	38	6.33 user: 6.33 utils per dollar spent				user: I will not use this combo because I have not maximized Marginal Utility	2	117	42	14.00
	3	121	33	5.50	3	153	36	12.00
	4	150	29	4.83	4	181	28	9.33
	5	175	25	4.17	5	206	25	8.33	Should you start buying movies year?
	6	196	21	3.50	6	225	19	6.33
	7	214	18	3.00	7	243	18	6.00
	8	229	15	2.50	8	260	17	5.67
	9	241	12	2.00	9	276	16	5.33
	10	250	9	1.50	10	291	15	5.00
	11	256	6	1.00	11	305	14	4.67
	12	259	3	0.50	12	318	13	4.33
	13	261	2	0.33	13	330	12	4.00	Buying More of one creates
	14	262	1	0.17	14	341	11	3.67	Diminshing Marginal Utility
									and Makes fewer of alternatives affordable.
	Movies				Pop
	Quantity	Total Utility	Marginal Utility	Price/MU	Quantity	Total Utility	Marginal Utility	Price/MU
	0	0	0		0	0	0
	1	50	50	0.12	1	75	75	0.04
	2	88	38	0.16	2	117	42	0.07
	3	121	33	0.18	3	153	36	0.08
	4	150	29	0.21	4	181	28	0.11
	5	175	25	0.24	5	206	25	0.12
	6	196	21	0.29	6	225	19	0.16
	7	214	18	0.33	7	243	18	0.17
	8	229	15	0.40	8	260	17	0.18
	9	241	12	0.50	9	276	16	0.19
	10	250	9	0.67	10	291	15	0.20
	11	256	6	1.00	11	305	14	0.21
	12	259	3	2.00	12	318	13	0.23
	13	261	2	3.00	13	330	12	0.25
	14	262	1	6.00	14	341	11	0.27	Diminshing Marginal Utility

Marginal Utility (2)

With a Budget of $30 For Only Two Activities
Cost Of A Movie = $6
Cost Of A ix Pack of Pop = $3
	Movies			Marginal Utility	Pop			Marginal Utility
	Quantity	Total Utility	Marginal Utility	Per Dollar Spent	Quantity	Total Utility	Marginal Utility	Per Dollar Spent
	0	0	0		0	0	0
	1	50	50	8.33	1	75	75	25.00
	2	88	38	6.33	2	117	42	14.00
	3	121	33	5.50	3	153	36	12.00
	4	150	29	4.83	4	181	28	9.33
	5	175	25	4.17	5	206	25	8.33
	6	196	21	3.50	6	225	19	6.33
	7	214	18	3.00	7	243	18	6.00
	8	229	15	2.50	8	260	17	5.67
	9	241	12	2.00	9	276	16	5.33
	10	250	9	1.50	10	291	15	5.00
	11	256	6	1.00	11	305	14	4.67
	12	259	3	0.50	12	318	13	4.33
	13	261	2	0.33	13	330	12	4.00
	14	262	1	0.17	14	341	11	3.67	Diminshing Marginal Utility
	Movies				Pop
	Quantity	Total Utility	Marginal Utility	Price/MU	Quantity	Total Utility	Marginal Utility	Price/MU
	0	0	0		0	0	0
	1	50	50	0.12	1	75	75	0.04
	2	88	38	0.16	2	117	42	0.07
	3	121	33	0.18	3	153	36	0.08
	4	150	29	0.21	4	181	28	0.11
	5	175	25	0.24	5	206	25	0.12
	6	196	21	0.29	6	225	19	0.16
	7	214	18	0.33	7	243	18	0.17
	8	229	15	0.40	8	260	17	0.18
	9	241	12	0.50	9	276	16	0.19
	10	250	9	0.67	10	291	15	0.20
	11	256	6	1.00	11	305	14	0.21
	12	259	3	2.00	12	318	13	0.23
	13	261	2	3.00	13	330	12	0.25
	14	262	1	6.00	14	341	11	0.27	Diminshing Marginal Utility

Marginal Utility Within Budget

Marginal Utility Per Dollar
Cost Of A Movie = $6
Cost Of A ix Pack of Pop = $3
Movies			Marginal Utility	Gain	Pop			Marginal Utility	Gain
QTY	Total Utility	Marginal Utility	Per Dollar Spent		QTY	Total Utility	Marginal Utility	Per Dollar Spent
0	0	0			0	0	0
1	50	50	8.33		2	117	42	14.00
2	88	38	6.33	2.00	4	181	28	9.33	4.67	Marginal Gain > Marginal Loss So Go To Next Step
3	121	33	5.50	0.83	6	225	19	6.33	3.00	Marginal Gain > Marginal Loss So Go To Next Step
4	150	29	4.83	0.67	8	260	17	5.67	0.67	Marginal Gain = Marginal Loss So Go To Previous Step
5	175	25	4.17	0.67	10	291	15	5.00	0.67
As Prices Change, the combination that creates maximum utility per dollar changes.
Thus, your maximize utility when Marginal Utility Per Dollar for one is equal to the Marginal Utility Per Dollar for the other.
Thus as prices change, the demand for each curve changes, thus giving each person their own demand curve for the product.

Marginal Utility Per $ (2)

Marginal Utility Per Dollar
Cost Of A Movie = $6
Cost Of A ix Pack of Pop = $3
Movies			Marginal Utility	Pop			Marginal Utility
QTY	Total Utility	Marginal Utility	Per Dollar Spent	QTY	Total Utility	Marginal Utility	Per Dollar Spent	Total Marg. Ut./$
0	0	0		10	291	15	5.00	5.00
1	50	50	8.33	8	260	17	5.67	14.00
2	88	38	6.33	6	225	19	6.33	12.67
3	121	33	5.50	4	181	28	9.33	14.83
4	150	29	4.83	2	117	42	14.00	18.83	Maximum Marginal Utility Per Dollar
5	175	25	4.17	0	0	0		4.17
As Prices Change, the combination that creates maximum utility per dollar changes.
Thus, your maximize utility when Marginal Utility Per Dollar for one is equal to the Marginal Utility Per Dollar for the other.
Thus as prices change, the demand for each curve changes, thus giving each person their own demand curve for the product.

Competition Continuum

Market Continuum

Imperfect Markets

PURE

MONOPOLISTIC COMPETITION

OLIGOPOLY

(DUOPOLY)

MONOPOLY

(PERFECT)

MACRS

	Research Equipment, race horses more than 2 years old, any other horse more than 12 years old when purchased, special tools of certain industries	Computers, typewriters, copiers, cars (non luxury), taxis, light general-purpose trucks, semi-conductor manufacturing equipment, computer based telephone central office switching equipment, qualified technological equipment, property used for R&D	Railroad track, Single-purpose agriculture (pigpens) or horticulture structures; fixtures, most manufacturing equipment, office furniture	Equipment used in refinement of petroleum, equipment used for manufacture of tabacco products and certain food products	Municipal wastewater treatment plants, telephone distribution plants and comparable equipment used for two-way exchange of data and voice communication	Municipal sewers	Residential rental property	Commercial real estate
	3	5	7	10	15	20	27.5	31.5
Year	Begins with 200% D. B.	Begins with 200% D. B.	Begins with 200% D. B.	Begins with 200% D. B.	Begins with 150% D. B.	Begins with 150% D. B.	All Straight Line	All Straight Line
1	33.00%	20.00%	14.28%	10.00%	5.00%	3.75%	3.70%	3.23%
2	45.00%	32.00%	24.49%	18.00%	9.50%	7.22%	3.70%	3.23%
3	15.00%	19.20%	17.49%	14.40%	8.55%	6.68%	3.70%	3.23%
4	7.00%	11.52%	12.49%	11.52%	7.69%	6.18%	3.70%	3.23%
5		11.52%	8.93%	9.22%	6.93%	5.71%	3.70%	3.23%
6		5.76%	8.93%	7.37%	6.23%	5.28%	3.70%	3.23%
7			8.93%	6.55%	5.90%	4.89%	3.70%	3.23%
8			4.46%	6.55%	5.90%	4.52%	3.70%	3.23%
9				6.55%	5.90%	4.46%	3.70%	3.23%
10				6.55%	5.90%	4.46%	3.70%	3.23%
11				3.29%	5.90%	4.46%	3.70%	3.23%
12					5.90%	4.46%	3.70%	3.23%
13					5.90%	4.46%	3.70%	3.23%
14					5.90%	4.46%	3.70%	3.23%
15					5.90%	4.46%	3.70%	3.23%
16					3.00%	4.46%	3.70%	3.23%
17						4.46%	3.70%	3.23%
18						4.46%	3.70%	3.23%
19						4.46%	3.70%	3.23%
20						4.46%	3.70%	3.23%
21	Bold numbers indicate the switch to straight line depreciation.					2.25%	3.70%	3.23%
22							3.70%	3.23%
23							3.70%	3.23%
24							3.70%	3.23%
25							3.70%	3.23%
26							3.70%	3.23%
27							3.70%	3.23%
28								3.23%
29								3.23%
30								3.23%
31								3.23%
	Since 1989 tax bill (Omnibus Budget Reconciliation Act of 1989), cell phones and similar equipment are no longer depreciated by MACRS but they are treated as "Listed Property", thus if used more than 50% for business use, straight-line method is required

Four-Firm Concentration

Top Four Concentration Ratios
	Monopoly	Oligopoly	Monopolistic Competition	Pure Competion
Sales (000,000) Firm 1	2,000	1,500	600	10
Sales (000,000) Firm 2	- 0	800	400	8
Sales (000,000) Firm 3	- 0	450	250	6
Sales (000,000) Firm 4	- 0	300	200	1
Total Sales of the Largest Firms	2,000	3,050	1,450	25
Remaining Firms	- 0	1,900	2,500	9,000
Industry Total	2,000	4,950	3,950	9,025
Four-Firm Concentration Ratio	100%	62%	37%	0.28%
		>60%	<=60%	<1%

Herfindahl-Hirschman Index

Herfindahl-Hirschman Index
	Monopoly 10,000	Oligopoly >1,000
Market Share Firm 1	100	45
Market Share Firm 2	- 0	25
Market Share Firm 3	- 0	15
Market Share Firm 4		10
Market Share Firm 5	- 0	5
Total Market Share	100	100
	1002	452+252+152+102+52
Herfindahl-Hirschman Index (HHI)	10,000	3,000
>1,000 and <1800 moderately competitive and will be scrutinized by the U.S. Justice Department Upon Merge
>1,800 = uncompetitive and will be challenged by the U.S. Justice Department Prior To Merge
<1,000 = highly competitive
Monopolistic Competition >100
Largest 30 Firms, each with 3% market share	=32x30=	270
Pure Competition <100
Lagest 50 Firms, each with .1% market share	=.12x50=	0.50

Four-Firm Concentration (Rev)

Concentration Ratios
	What Market	What Market	What Market
	A	B	C
Sales (000) Firm 1	100	500	10
Sales (000) Firm 2	95	400	8
Sales (000) Firm 3	85	250	6
Sales (000) Firm 4	70	200	1
Total Sales of the Largest Firms	350	1,350	25
Remaining Firms	1,900	2,500	9,000
Industry Total	2,250	3,850	9,025
Four-Firm Concentration Ratio	16%	35%	0.28%
	<60% >1%	<60% >1%	<1%
	Monopolistic Comp	Monopolistic Comp	Pure Competition

HHI (Review)

Herfindahl-Hirschman Index
	Monopoly 10,000	Oligopoly >1,000
Market Share Firm 1	100	25
Market Share Firm 2	- 0	20
Market Share Firm 3	- 0	15
Market Share Firm 4		15
Market Share Firm 5		10
Market Share Firm 6	- 0	15
Total Market Share	100	100
	10,000	1,800
	Monopoly

Test One Tally

Multiple Choice Right	42	Problems Right	31
Multiple Choice Points	84	Points for Problems	93	Total Points	177
				Possible Right	212
				Score	83.49%

Marginal Physical Product

Marginal Physical Product
Scenario	Labor (workers per day)	Units Produced	Marginal Physical Product	Average Product (Per Worker)	Labor @$25 Per Day
A	0	0	0
B	1	4	4	4.00	$ 6.25
C	2	10	6	5.00	$ 5.00
D	3	13	3	4.33	$ 5.77
E	4	15	2	3.75	$ 5.00
F	5	16	1	3.20	$ 4.69

Total Product Curve

A B C D E F 0 4 10 13 15 16

Marginal Physical Product

A B C D E F 0 4 6 3 2 1

Short-Run Cost

Marginal Physical Product And Costs
Scenario	Labor (workers per day)	Total Output (Units Produced)	Marginal Physical Product	Total Fixed Cost	Total Variable Cost (Wage/Day/Worker @$25)	Total Cost	Labor Marginal Cost	Marginal Cost (Per Unit of Output) John Herzog: The increase of cost that results from a one-unit increase in output.	Average Fixed Cost	Average Variable Cost (Per Sweater)	Average Total Cost (Per Sweater)	Marginal Revenue Product (@ Price of $18)
A	0	0	N/A	$ 25.00	$ - 0	$ 25.00
B	1	4	4	$ 25.00	$ 25.00	$ 50.00	$ 25.00	$ 6.25	$ 6.25	$ 6.25	$ 12.50	$ 72.00
C	2	10	6	$ 25.00	$ 50.00	$ 75.00	$ 25.00	$ 4.17	$ 2.50	$ 5.00	$ 7.50	$ 108.00
D	3	13	3	$ 25.00	$ 75.00	$ 100.00	$ 25.00	$ 8.33	$ 1.92	$ 5.77	$ 7.69	$ 54.00
E	4	15	2	$ 25.00	$ 100.00	$ 125.00	$ 25.00	$ 12.50	$ 1.67	$ 6.67	$ 8.33	$ 36.00
F	5	16	1	$ 25.00	$ 125.00	$ 150.00	$ 25.00	$ 25.00	$ 1.56	$ 7.81	$ 9.38	$ 18.00

Marginal Cost Curve

6.25 4.166666666666667 8.3333333333333339 12.5 25

Items Produced

Marginal Costs

All Cost Chart

Labor (workers per day) Marginal Physical Product Marginal Cost (Per Unit of Output) Average Fixed Cost Average Variable Cost (Per Sweater) Average Total Cost (Per Sweater) Marginal Revenue Product (@ Price $30 ea.) 0 0 0 Labor (workers per day) Marginal Physical Product Marginal Cost (Per Unit of Output) Average Fixed Cost Average Variable Cost (Per Sweater) Average Total Cost (Per Sweater) Marginal Revenue Product (@ Price $30 ea.) 1 6 13.333333333333334 16.666666666666668 13.333333333333334 30 180 Labor (workers per day) Marginal Physical Product Marginal Cost (Per Unit of Output) Average Fixed Cost Average Variable Cost (Per Sweater) Average Total Cost (Per Sweater) Marginal Revenue Product (@ Price $30 ea.) 2 9 8.8888888888888893 6.666666666666667 10.666666666666666 17.333333333333332 270 Labor (workers per day) Marginal Physical Product Marginal Cost (Per Unit of Output) Average Fixed Cost Average Variable Cost (Per Sweater) Average Total Cost (Per Sweater) Marginal Revenue Product (@ Price $30 ea.) 3 5 16 5 12 17 150 Labor (workers per day) Marginal Physical Product Marginal Cost (Per Unit of Output) Average Fixed Cost Average Variable Cost (Per Sweater) Average Total Cost (Per Sweater) Marginal Revenue Product (@ Price $30 ea.) 4 3 26.666666666666668 4.3478260869565215 13.913043478260869 18.260869565217391 90 Labor (workers per day) Marginal Physical Product Marginal Cost (Per Unit of Output) Average Fixed Cost Average Variable Cost (Per Sweater) Average Total Cost (Per Sweater) Marginal Revenue Product (@ Price $30 ea.) 5 2 40 4 16 20 60 Labor (workers per day) Marginal Physical Product Marginal Cost (Per Unit of Output) Average Fixed Cost Average Variable Cost (Per Sweater) Average Total Cost (Per Sweater) Marginal Revenue Product (@ Price $30 ea.) 6 1 80 3.8461538461538463 18.46153846153846 22.307692307692307 30

Short-Run Cost (Review)

Short-Run Costs
Scenario	Labor (workers per day)	Units Produced	Marginal Physical Product	Total Fixed Cost	Total Variable Cost (Wage/Day/Worker @$80)	Total Cost	Marginal Cost	Marginal Cost (Per Unit of Output) John Herzog: The increase of cost that results from a one-unit incrase in output.	Average Fixed Cost	Average Variable Cost (Per Sweater)	Average Total Cost (Per Sweater)	Marginal Revenue Product (@ Price $30 ea.)
A	0	0	0	100	0	100						- 0	0
B	1	6	6	100	80	180	80	13.33	16.67	13.33	30.00	180.00	4
C	2	15	9	100	160	260	80	8.89	6.67	10.67	17.33	270.00	10
D	3	20	5	100	240	340	80	16.00	5.00	12.00	17.00	150.00	13
E	4	23	3	100	320	420	80	26.67	4.35	13.91	18.26	90.00	15
F	5	25	2	100	400	500	80	40.00	4.00	16.00	20.00	60.00	16
G	6	26	1	100	480	580	80	80.00	3.85	18.46	22.31	30.00

Marginal Cost Curve

0 4 10 13 15 16 13.333333333333334 8.8888888888888893 16 26.666666666666668 40

Items Produced

Marginal Costs

Short-Run Cost (Review) (2)

Short-Run Costs
Scenario	Labor (workers per Hour	Units Produced	Marginal Physical Product	Total Fixed Cost	Total Variable Cost (Wage/Hour/Worker @$10)	Total Cost	Marginal Cost	Marginal Cost (Per Unit of Output) John Herzog: The increase of cost that results from a one-unit incrase in output.	Average Fixed Cost	Average Variable Cost (Per Sweater)	Average Total Cost (Per Sweater)	Marginal Revenue Product (@ Price $8 ea.)
A	0	0	0	100	0	100						- 0	0
B	1	5	5	100	10	110	10	2.00	20.00	2.00	22.00	40.00	4
C	2	12	7	100	20	120	10	1.43	8.33	1.67	10.00	56.00	10
D	3	18	6	100	30	130	10	1.67	5.56	1.67	7.22	48.00	13
E	4	23	5	100	40	140	10	2.00	4.35	1.74	6.09	40.00	15
F	5	27	4	100	50	150	10	2.50	3.70	1.85	5.56	32.00	16
G	6	30	3	100	60	160	10	3.33	3.33	2.00	5.33	24.00

Marginal Cost Curve

0 4 10 13 15 16 2 1.4285714285714286 1.6666666666666667 2 2.5

Items Produced

Marginal Costs

There Are No Fixed Costs

There Are No Fixed Costs In The Long Run
F
I
X
E
D
C
O
S
T
S
		Demand/Volume
	Breakpoints-More capital inputs needed

Economies of Scale

Behavior of Long Term Costs
	Economies of Scale-Features of a firm's technology that leads to a falling long-run average total costs as output increases
A
v
e
r
a
g
e
T
o
t
a
l
C
o
s
t
			Output
		Change In Combination of Inputs

DisEconomies of Scale

Behavior of Long Term Costs
	Economies of Scale-Features of a firm's technology that leads to a falling long-run average total costs as output increases
A
v
e
r
a
g
e
T
o
t
a
l
C
o
s
t
			Output
		Change In Combination of Inputs

Return To Scale

Behavior of Long Term Costs
	Economies of Scale-Features of a firm's technology that leads to a falling long-run average total costs as output increases
A
v
e
r
a
g
e
T
o
t
a
l
C
o
s
t
			Output
		Change In Combination of Inputs

Demand Curves-Marginal Revenue

Monopoly and Monopolistic Competition Demand And Marginal Revenue Curves.
				9	1
Price	Quantity Demanded	Total Revenue	Marginal Revenue	8	2
$ 9	1	$ 9	$ 9	7	3
$ 8	2	$ 16	$ 7	6	4
$ 7	3	$ 21	$ 5	5	5
$ 6	4	$ 24	$ 3	4	6
$ 5	5	$ 25	$ 1	3	7
$ 4	6	$ 24	$ (1)	2	8
$ 3	7	$ 21	$ (3)	1	9
$ 2	8	$ 16	$ (5)
$ 1	9	$ 9	$ (7)

Demand Curve Vs. Margainal Revenue

1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 9 7 5 3 1 -1 -3 -5 -7

Quantity Demanded

Price/Marginal Revenue

Marginal Cost

Profit Maximization

Demand Curve

Marginal Revenue Curve

Demand-Marg Rev Perf Inelastic

Monopoly and Monopolistic Competition Demand And Marginal Revenue Curves.
						9	1
Price	Quantity Demanded	Marginal Revenue	Total Revenue	9		8	2
$ 9	10		$ 90	8		7	3
$ 8	10	$ (10)	$ 80	7		6	4
$ 7	10	$ (10)	$ 70	6		5	5
$ 6	10	$ (10)	$ 60	5		4	6
$ 5	10	$ (10)	$ 50	4		3	7
$ 4	10	$ (10)	$ 40	3		2	8
$ 3	10	$ (10)	$ 30	2		1	9
$ 2	10	$ (10)	$ 20	1
$ 1	10	$ (10)	$ 10	0	10
				-1
				-2
				-3
				-4
				-5
				-6
				-7
				-8
				-9
				-10

Diff Markets Curves

Pure Competition

Oligopolies

Monopoly and Monopolistic Competition.

Price

MR = D =P

Quantity Demanded

Demand Curves (Diff Markets)

Pure Competition

Oligopolies

Monopoly and Monopolistic Competition.

Price

Quantity Demanded

More MR Curves

							Price	QD	Rev.	Marginal Revenue
							$ 100.00	1	100	$ 100.00
Price			Price			$ 100.00	$ 1.00	1	1	$ (99.00)
	MR = D
						$ 1.00
		Quantity Demanded		Quantity Demanded	Quantity Demanded		Quantity Demanded
						b

Pure Comp Supply

Price

Pure Comp Demand Curves

	Individual		Market
Price		Price
	MR = D

Oligopoly Demand Curve

			Oligopolies
Price
					Original Demand Due to Price Drops
15000
12000
11000
						Demand Curve Before Retaliation
		New Demand After Retaliation
					Demand Curve After Retaliation
	1 Million		2 Million
				Quantity Demanded

Oligopoly Demand Curve (2)

		Oligopolies
Price
15000
12000
11000
				Demand Curve After Retaliation
	1 Million	2 Million
			Quantity Demanded

Oligopoly Demand MR

			Oligopolies
Price
15000
12000
11000		GAP
							Demand Curve Before Retaliation
						Marginal Revenue Curve of Demand Curve Before Retaliation
						Demand Curve After Retaliation
				Marginal Revenue Curve of Demand Curve After Retaliation
	1 Million		2 Million
					Quantity Demanded

Oligopoly MR

			Oligopolies
Price
		Marginal Cost Curves
15000
			Marginal Revenue Curve of Demand Curve Before Retaliation
12000
11000			GAP	Profit Maximization: MR=MC exists at any one of the intersections.
				Marginal Revenue Curve of Demand Curve After Retaliation
	1 Million		2 Million
					Quantity Demanded

Demand Curves-Marginal Reve (2)

Monopoly and Monopolistic Competition Demand And Marginal Revenue Curves.
				9	1
Price	Quantity Demanded	Total Revenue	Marinal Revenue	8	2
$ 700	200	$ 140,000		7	3
$ 600	400	$ 240,000	$ 100,000	6	4
$ 500	600	$ 300,000	$ 60,000	5	5
$ 400	800	$ 320,000	$ 20,000	4	6
$ 300	1100	$ 330,000	$ 10,000	3	7
				2	8
				1	9

Demand Curve Vs. Margainal Revenue

1 2 3 4 5 6 7 8 9 700 600 500 400 300 1 2 3 4 5 6 7 8 9 100000 60000 20000 10000

Quantity Demanded

Price/Marginal Revenue

Marginal Cost

Profit Maximization

Demand Curve

Marginal Revenue Curve

MR MC Production Decision

Scenario	Price	Qty. Demanded	Total Revenue	Marginal Revenue	Marginal Cost
A	$ 15.00	5	$ 75.00		$ 10.00
B	$ 14.00	6	$ 84.00	$ 9.00	$ 8.00
C	$ 13.00	7	$ 91.00	$ 7.00	$ 7.00
D	$ 12.00	8	$ 96.00	$ 5.00	$ 8.00
E	$ 11.00	9	$ 99.00	$ 3.00	$ 9.00

Perfect Competition Production

				Perfect Competition
Price
							P=MR
							MC=MR
								Maximum Output
	1	2	3	4	5	6	7
						Quantity Demanded

Labor Supply Curve(BackBending)

Labor Supply Curve (Backward Bending)
		Income Effect
Wages
		Substitution Effect
	Labor (hours per day)

Marginal REvenue Product

Marginal Revenue Product
Scenario	Labor (workers per day)	Units Produced	Marginal Physical Product	Marginal Revenue Product @ Price of $8 each
A	0	0	0	$ - 0
B	1	4	4	$ 32.00
C	2	10	6	$ 48.00
D	3	13	3	$ 24.00
E	4	15	2	$ 16.00
F	5	16	1	$ 8.00
Do not hire worker 5, if the going wage is $8 or more.

Hiring Decision

MRP
10
9
8
7
6
5										Wage Rate
4
3
2
1
0	1	2	3	4	5	6	7	8	9
				Quantity of Labor (Workers hired per hour)

Cost Efficiency

Strawberry Farm
Marginal Physical Product For Labor of Newest Worker	=	5	(Boxes Per Hour)	=	1.25 boxes per $1 of cost
Cost of Labor For New Worker	=	$4.00	(Per Hour)
Marginal Physical Product Of Mechanical Stawberry Picker	=	10	(Boxes Per Hour)	=	1 box per $1 of cost
Cost of mechanical picker (rent/operating labor)	=	$10.00	Per Hour

Best Process

Process A					Output
	Labor	400 hours @ $4 per hour	$ 1,600.00		5000 units	$ 0.4460	Each.
	Land	1 acre rent during the given time period @$500	$ 500.00
	Capital	13 hours @ $10 per hour	$ 130.00
		Total Cost	$ 2,230.00
Process B
	Labor	270 hours @ $4 per hour	$ 1,080.00		5000 units	$ 0.3460	Each.
	Land	1 acre rent during the given time period @$500	$ 500.00
	Capital	15 hours @ $10 per hour	$ 150.00
		Total Cost	$ 1,730.00
Process C
	Labor	220 hours @ $4 per hour	$ 880.00	BEST	5000 units	$ 0.3120	Each.
	Land	1 acre rent during the given time period @$500	$ 500.00
	Capital	18 hours @ $10 per hour	$ 180.00
		Total Cost	$ 1,560.00
Process D				The scenarios will go up in costs if you have too much equipment and not enough workers to run them.
	Labor	180 hours @ $4 per hour	$ 720.00		5000 units	$ 0.3140	Each.
	Land	1 acre rent during the given time period @$500	$ 500.00
	Capital	35 hours @ $10 per hour	$ 350.00
		Total Cost	$ 1,570.00

Best Process (Review)

Process A		Output	Hours	Rate
	Labor	10,000 Units	325	$ 5.00	$ 1,625.00
	Land			$ 700	$ 700.00
	Capital		13	$ 15.00	$ 195.00
					$ 2,520.00
Process B
	Labor	10,000 Units	250	$ 5.00	$ 1,250.00
	Land			$ 700	$ 700.00
	Capital		15	$ 15.00	$ 225.00
					$ 2,175.00
Process C
	Labor	10,000 Units	200	$ 5.00	$ 1,000.00	BEST
	Land			$ 700	$ 700.00
	Capital		30	$ 15.00	$ 450.00
					$ 2,150.00
Process D		The scenarios will go up in costs if you have too much equipment and not enough workers to run them.
	Labor	10,000 Units	180	$ 5.00	$ 900.00
	Land			$ 700	$ 700.00
	Capital		45	$ 15.00	$ 675.00
					$ 2,275.00

Maringal FACTOR Cost

Scenario	Wage Rate/Hour	X	Quantity of Labor Supplied (workers per hour)	Total Wage Cost	Marginal Factor Cost (per labor-hour)
A	$ - 0		0	$ - 0
B	$ 1.00		0	$ - 0
C	$ 5.00		1	$ 5.00	$ 5.00
D	$ 6.00		2	$ 12.00	$ 7.00
E	$ 7.00		3	$ 21.00	$ 9.00
F	$ 8.00		4	$ 32.00	$ 11.00
G	$ 9.00		5	$ 45.00	$ 13.00

Financial Intermediaries

Private Placement	Investor				Needers of funds
Financial Markets	Investor		Financial Markets		Needers of funds
Financial Institutions	Investor	Financial Institutions	Financial Markets	Financial Institutions	Needers of funds

Dow Jones Original Eleven

$ 20.00
$ 20.00
$ 20.00
$ 10.00
$ 20.00
$ 20.00
$ 20.00
$ 20.00
$ 20.00
$ 20.00
$ 20.00
$ 20.00	Average

Systematic and Non System Risks

R
I
S
K
				Diversifiable (Non-Systematic)
			Systematic (Non Diversifiable)
	0
		Number of firms, industries, countries, firm sizes, and vehicles you invest in.

PV of Lump Sum(s)

Future Value
1000 Investment @10% Compounded Annually for three years Gave US A FV of $1,331
10001.101.10*1.10
1000*(1.10)3
=$1,331
Present Value is asking "What is value today of money to be received later?"
PV Concept
PVIF = 1/FVIF
X*1.331=$1,331
X=$1,331/1.331
X=$1,000
X=1331*(1/1.331)
X=1331*.751
X=1331*(1/(1+(.10/1))^3)
Investment Yields $12,000 ten years from now and if like investment has Kr of 8% Compounded Annually
$ 5,556.00	Present Value
Investment Yields $12,000 ten years from now and if like investment has Kr of 9% Compounded Annually
$ 5,064.00	Present Value
Investment Yields $12,000 ten years from now and if like investment has Kr of 8% Compounded Semi Annually
$ 5,472.00	Present Value
Investment Yields $12,000 ten years from now and if like investment has Kr of 9% Compounded Semi-Annually
2.4117	0.4146	$ 4,975.71
FVIF	PVIF	Present Value
What is the PV of the cash flows below to be received, Kr = 7% Compounded Annually
	0	1	2	3
		$ 4,000	$ 5,000	$ 8,000
=4000*.935	$ 3,740
=5000*.873	$ 4,365
=8000*.816	$ 6,528
	$ 14,633
			Discount Rate/ Kr	7%	Comp.	1
			PVIF
	A-2 Finds PV of Lump Sums to be received.
			7%
1			0.935
2			0.873
3			0.816
	0	1	2	3
		$ 5,000	$ 5,000	$ 5,000
=5000*.935	$ 4,675
=5000*.873	$ 4,365
=5000*.816	$ 4,080
	$ 13,120
			Discount Rate/ Kr	7%	Comp.	1
			PVIF
	A-2 Finds PV of Lump Sums to be received.
			7%
1			0.935
2			0.873
3			0.816
			2.624	2.624*5,000	$ 13,120

Project Analysis 10%

PROJECT ANALYSIS
	A	B
Initital Investment	$ 42,000	$ 45,000
Year 1	$ 14,000	$ 28,000
Year 2	$ 14,000	$ 12,000
Year 3	$ 14,000	$ 10,000
Year 4	$ 14,000	$ 10,000
Year 5	$ 14,000	$ 10,000
Average	$ 14,000	$ 14,000
Total	$ 70,000	$ 70,000
Net Present Value
Kr or Discount Rate=	10%
PVIFA 10%,5-Table A-4	3.791		PVIF 10%,5 A-2
Annuity	$ 14,000	$ 28,000	0.909	25,452.00
PV	$ 53,074	$ 12,000	0.826	9,912.00
NPV	$ 11,074	$ 10,000	0.751	7,510.00
		$ 10,000	0.683	6,830.00
		$ 10,000	0.621	6,210.00
				55,914.00
			NPV	10,914.00
INTERNAL RATE OF RETURN (IRR)
The rate of return on an investment in a project.

Project Analysis (12%)

PROJECT ANALYSIS
	A	B	B
Initital Investment	$ 42,000	$ 45,000
			Cash Certainty Ratio
Year 1	$ 14,000	$ 28,000	95%
Year 2	$ 14,000	$ 12,000	90%
Year 3	$ 14,000	$ 10,000	85%
Year 4	$ 14,000	$ 10,000	85%
Year 5	$ 14,000	$ 10,000	70%
Average	$ 14,000	$ 14,000
Total	$ 70,000	$ 70,000
Net Present Value
Kr or Discount Rate=	12%						Rf Rate = 6%
PVIFA 12%,5-Table A-4	3.605		PVIF 12%,5 A-2				Cash Certainty Ratio	Cash Certainty Equivalent
Annuity	$ 14,000	$ 28,000	0.893	25,000.00	$ 28,000	X	95%	$ 26,600	X	0.943	$ 25,083.80
PV	$ 50,470	$ 12,000	0.797	9,566.33	$ 12,000	X	90%	$ 10,800	X	0.889	$ 9,601.20
NPV	$ 8,470	$ 10,000	0.712	7,117.80	$ 10,000	X	85%	$ 8,500	X	0.839	$ 7,131.50
		$ 10,000	0.636	6,355.18	$ 10,000	X	85%	$ 8,500	X	0.792	$ 6,732.00
		$ 10,000	0.567	5,674.27	$ 10,000	X	70%	$ 7,000	X	0.747	$ 5,229.00
				53,713.58							$ 53,777.50
			NPV	8,713.58						NEW NPV	$ 8,777.50
INTERNAL RATE OF RETURN (IRR)
The rate of return on an investment in a project.
	Project A			Project B.
	20%			22%

More Project Analsysis

PROJECT ANALYSIS
			NPV
		Kr	A	B
		0	$28,000	$25,000
IRR		10%	$11,074	$10,914
		20%	$0	$0
		22%	$0	$0
RADR	Project A
Initial Investment	$ 42,000	PVIFA13%,5
Year 1	$ 14,000	3.517
Year 2	$ 14,000	X $14,000
Year 3	$ 14,000	$ 49,238	PV
Year 4	$ 14,000	$ 7,238	NPV
Year 5	$ 14,000
Total	$ 70,000
Average	$ 14,000
	Project B
Initial Investment	$ 45,000	PVIF 18%
Year 1	$ 28,000	0.847	$ 23,728.81
Year 2	$ 12,000	0.718	$ 8,618.21
Year 3	$ 10,000	0.609	$ 6,086.31
Year 4	$ 10,000	0.516	$ 5,157.89
Year 5	$ 10,000	0.437	$ 4,371.09
Total	$ 70,000		$ 47,962.32	PV
Average	$ 14,000	NPV	$ 2,962.32
Breakeven Cash Flow (Per Year)
Initial Investment=	$ 250,000
Kr=	15%
Years	10
	Cf(PVIFA,15%,10)=$250,000
	Cf(5.019)=$250,000
	Breakeven CF=	$ 49,810.72
Review
Breakeven Cash Flow (Per Year)
Initial Investment=	$ 475,000
Kr=	12%
Years	20
	Cf(PVIFA,12%,20)=$475,000
	Cf(7.469)=$475,000
	Breakeven CF=	$ 63,596.20

NPV Chart Line

	30
N		A					NPV
P						Kr	A	B
V	25					0	$28,000	$25,000
		B				10%	$11,074	$10,914
						20%	$0
	20					22%	$0	$0
	15
	10
	0
			5		10	13%	15		20	25	B
											A
				Discount Rates

Project Analysis (Review)

PROJECT ANALYSIS					Project C Cash Certainty Equiv.			Rf=5%
	A	B	C
Initital Investment	$ 60,000	$ 50,000	$ 45,000
						CCE		PVIF
Year 1	$ 20,000	$ 28,000	$ 30,000	X	98%	$ 29,400	X	0.952	$ 28,000
Year 2	$ 20,000	$ 12,000	$ 15,000	X	90%	$ 13,500	X	0.907	$ 12,245
Year 3	$ 20,000	$ 10,000	$ 10,000	X	87%	$ 8,700	X	0.864	$ 7,515
Year 4	$ 20,000	$ 10,000	$ 7,500	X	80%	$ 6,000	X	0.823	$ 4,936
Year 5	$ 20,000	$ 10,000	$ 7,500	X	70%	$ 5,250	X	0.784	$ 4,114
Average	$ 20,000	$ 14,000	$ 14,000					Adjusted PV	$ 56,810
Total	$ 100,000	$ 70,000	$ 70,000					Adjusted NPV	$ 11,810
Net Present Value
Kr or Discount Rate=	12%	Project B
PVIFA 12%,5-Table A-4	3.605		PVIF 12%,5 A-2
Annuity X	$ 20,000	$ 28,000	0.893	25,000.00					NPV
PV	$ 72,100	$ 12,000	0.797	9,566.33				Kr	A	B
Initial Investment -	$ 60,000	$ 10,000	0.712	7,117.80				0	$40,000	$20,000
NPV	$ 12,100	$ 10,000	0.636	6,355.18				12%	$12,100	$3,714
		$ 10,000	0.567	5,674.27				20%	$0
				53,713.58				22%		$0
			NPV	3,713.58
INTERNAL RATE OF RETURN (IRR)
The rate of return on an investment in a project.
	Project A			Project B.
	20%			22%

A-1 A-2

	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%	11%	12%	13%	14%	15%	16%	17%	18%	19%	20%	21%	22%	23%	24%	25%	26%	27%	28%	29%	30%
A-1, FVIF
Periods
1	1.010	1.020	1.030	1.040	1.050	1.060	1.070	1.080	1.090	1.100	1.110	1.120	1.130	1.140	1.150	1.160	1.170	1.180	1.190	1.200	1.210	1.220	1.230	1.240	1.250	1.260	1.270	1.280	1.290	1.300
2	1.020	1.040	1.061	1.082	1.103	1.124	1.145	1.166	1.188	1.210	1.232	1.254	1.277	1.300	1.323	1.346	1.369	1.392	1.416	1.440	1.464	1.488	1.513	1.538	1.563	1.588	1.613	1.638	1.664	1.690
3	1.030	1.061	1.093	1.125	1.158	1.191	1.225	1.260	1.295	1.331	1.368	1.405	1.443	1.482	1.521	1.561	1.602	1.643	1.685	1.728	1.772	1.816	1.861	1.907	1.953	2.000	2.048	2.097	2.147	2.197
4	1.041	1.082	1.126	1.170	1.216	1.262	1.311	1.360	1.412	1.464	1.518	1.574	1.630	1.689	1.749	1.811	1.874	1.939	2.005	2.074	2.144	2.215	2.289	2.364	2.441	2.520	2.601	2.684	2.769	2.856
5	1.051	1.104	1.159	1.217	1.276	1.338	1.403	1.469	1.539	1.611	1.685	1.762	1.842	1.925	2.011	2.100	2.192	2.288	2.386	2.488	2.594	2.703	2.815	2.932	3.052	3.176	3.304	3.436	3.572	3.713
6	1.062	1.126	1.194	1.265	1.340	1.419	1.501	1.587	1.677	1.772	1.870	1.974	2.082	2.195	2.313	2.436	2.565	2.700	2.840	2.986	3.138	3.297	3.463	3.635	3.815	4.002	4.196	4.398	4.608	4.827
7	1.072	1.149	1.230	1.316	1.407	1.504	1.606	1.714	1.828	1.949	2.076	2.211	2.353	2.502	2.660	2.826	3.001	3.185	3.379	3.583	3.797	4.023	4.259	4.508	4.768	5.042	5.329	5.629	5.945	6.275
8	1.083	1.172	1.267	1.369	1.477	1.594	1.718	1.851	1.993	2.144	2.305	2.476	2.658	2.853	3.059	3.278	3.511	3.759	4.021	4.300	4.595	4.908	5.239	5.590	5.960	6.353	6.768	7.206	7.669	8.157
9	1.094	1.195	1.305	1.423	1.551	1.689	1.838	1.999	2.172	2.358	2.558	2.773	3.004	3.252	3.518	3.803	4.108	4.435	4.785	5.160	5.560	5.987	6.444	6.931	7.451	8.005	8.595	9.223	9.893	10.604
10	1.105	1.219	1.344	1.480	1.629	1.791	1.967	2.159	2.367	2.594	2.839	3.106	3.395	3.707	4.046	4.411	4.807	5.234	5.695	6.192	6.727	7.305	7.926	8.594	9.313	10.086	10.915	11.806	12.761	13.786
11	1.116	1.243	1.384	1.539	1.710	1.898	2.105	2.332	2.580	2.853	3.152	3.479	3.836	4.226	4.652	5.117	5.624	6.176	6.777	7.430	8.140	8.912	9.749	10.657	11.642	12.708	13.862	15.112	16.462	17.922
12	1.127	1.268	1.426	1.601	1.796	2.012	2.252	2.518	2.813	3.138	3.498	3.896	4.335	4.818	5.350	5.936	6.580	7.288	8.064	8.916	9.850	10.872	11.991	13.215	14.552	16.012	17.605	19.343	21.236	23.298
13	1.138	1.294	1.469	1.665	1.886	2.133	2.410	2.720	3.066	3.452	3.883	4.363	4.898	5.492	6.153	6.886	7.699	8.599	9.596	10.699	11.918	13.264	14.749	16.386	18.190	20.175	22.359	24.759	27.395	30.288
14	1.149	1.319	1.513	1.732	1.980	2.261	2.579	2.937	3.342	3.797	4.310	4.887	5.535	6.261	7.076	7.988	9.007	10.147	11.420	12.839	14.421	16.182	18.141	20.319	22.737	25.421	28.396	31.691	35.339	39.374
15	1.161	1.346	1.558	1.801	2.079	2.397	2.759	3.172	3.642	4.177	4.785	5.474	6.254	7.138	8.137	9.266	10.539	11.974	13.590	15.407	17.449	19.742	22.314	25.196	28.422	32.030	36.062	40.565	45.587	51.186
16	1.173	1.373	1.605	1.873	2.183	2.540	2.952	3.426	3.970	4.595	5.311	6.130	7.067	8.137	9.358	10.748	12.330	14.129	16.172	18.488	21.114	24.086	27.446	31.243	35.527	40.358	45.799	51.923	58.808	66.542
17	1.184	1.400	1.653	1.948	2.292	2.693	3.159	3.700	4.328	5.054	5.895	6.866	7.986	9.276	10.761	12.468	14.426	16.672	19.244	22.186	25.548	29.384	33.759	38.741	44.409	50.851	58.165	66.461	75.862	86.504
18	1.196	1.428	1.702	2.026	2.407	2.854	3.380	3.996	4.717	5.560	6.544	7.690	9.024	10.575	12.375	14.463	16.879	19.673	22.901	26.623	30.913	35.849	41.523	48.039	55.511	64.072	73.870	85.071	97.862	112.455
19	1.208	1.457	1.754	2.107	2.527	3.026	3.617	4.316	5.142	6.116	7.263	8.613	10.197	12.056	14.232	16.777	19.748	23.214	27.252	31.948	37.404	43.736	51.074	59.568	69.389	80.731	93.815	108.890	126.242	146.192
20	1.220	1.486	1.806	2.191	2.653	3.207	3.870	4.661	5.604	6.727	8.062	9.646	11.523	13.743	16.367	19.461	23.106	27.393	32.429	38.338	45.259	53.358	62.821	73.864	86.736	101.721	119.145	139.380	162.852	190.050
21	1.232	1.516	1.860	2.279	2.786	3.400	4.141	5.034	6.109	7.400	8.949	10.804	13.021	15.668	18.822	22.574	27.034	32.324	38.591	46.005	54.764	65.096	77.269	91.592	108.420	128.169	151.314	178.406	210.080	247.065
22	1.245	1.546	1.916	2.370	2.925	3.604	4.430	5.437	6.659	8.140	9.934	12.100	14.714	17.861	21.645	26.186	31.629	38.142	45.923	55.206	66.264	79.418	95.041	113.574	135.525	161.492	192.168	228.360	271.003	321.184
23	1.257	1.577	1.974	2.465	3.072	3.820	4.741	5.871	7.258	8.954	11.026	13.552	16.627	20.362	24.891	30.376	37.006	45.008	54.649	66.247	80.180	96.889	116.901	140.831	169.407	203.480	244.054	292.300	349.593	417.539
24	1.270	1.608	2.033	2.563	3.225	4.049	5.072	6.341	7.911	9.850	12.239	15.179	18.788	23.212	28.625	35.236	43.297	53.109	65.032	79.497	97.017	118.205	143.788	174.631	211.758	256.385	309.948	374.144	450.976	542.801
25	1.282	1.641	2.094	2.666	3.386	4.292	5.427	6.848	8.623	10.835	13.585	17.000	21.231	26.462	32.919	40.874	50.658	62.669	77.388	95.396	117.391	144.210	176.859	216.542	264.698	323.045	393.634	478.905	581.759	705.641
26	1.295	1.673	2.157	2.772	3.556	4.549	5.807	7.396	9.399	11.918	15.080	19.040	23.991	30.167	37.857	47.414	59.270	73.949	92.092	114.475	142.043	175.936	217.537	268.512	330.872	407.037	499.916	612.998	750.468	917.333
27	1.308	1.707	2.221	2.883	3.733	4.822	6.214	7.988	10.245	13.110	16.739	21.325	27.109	34.390	43.535	55.000	69.345	87.260	109.589	137.371	171.872	214.64	267.57	332.95	413.59	512.87	634.89	784.64	968.10	1192.53
28	1.321	1.741	2.288	2.999	3.920	5.112	6.649	8.627	11.167	14.421	18.580	23.884	30.633	39.204	50.066	63.800	81.134	102.967	130.411	164.845	207.965	261.86	329.11	412.86	516.99	646.21	806.31	1004.34	1248.85	1550.29
29	1.335	1.776	2.357	3.119	4.116	5.418	7.114	9.317	12.172	15.863	20.624	26.750	34.616	44.693	57.575	74.009	94.927	121.501	155.189	197.814	251.638	319.47	404.81	511.95	646.23	814.23	1024.02	1285.55	1611.02	2015.38
30	1.348	1.811	2.427	3.243	4.322	5.743	7.612	10.063	13.268	17.449	22.892	29.960	39.116	50.950	66.212	85.850	111.065	143.371	184.675	237.376	304.482	389.76	497.91	634.82	807.79	1025.93	1300.50	1645.50	2078.22	2620.00
31	1.361	1.848	2.500	3.373	4.538	6.088	8.145	10.868	14.462	19.194	25.410	33.555	44.201	58.083	76.144	99.586	129.946	169.177	219.764	284.852	368.423	475.50	612.43	787.18	1009.74	1292.67	1651.64	2106.25	2680.90	3405.99
32	1.375	1.885	2.575	3.508	4.765	6.453	8.715	11.737	15.763	21.114	28.206	37.582	49.947	66.215	87.565	115.520	152.036	199.629	261.519	341.822	445.792	580.12	753.29	976.10	1262.18	1628.76	2097.58	2695.99	3458.36	4427.79
33	1.389	1.922	2.652	3.648	5.003	6.841	9.325	12.676	17.182	23.225	31.308	42.092	56.440	75.485	100.700	134.003	177.883	235.563	311.207	410.186	539.408	707.74	926.55	1210.36	1577.72	2052.24	2663.93	3450.87	4461.29	5756.13
34	1.403	1.961	2.732	3.794	5.253	7.251	9.978	13.690	18.728	25.548	34.752	47.143	63.777	86.053	115.805	155.443	208.123	277.964	370.337	492.224	652.683	863.44	1139.66	1500.85	1972.15	2585.82	3383.19	4417.12	5755.06	7482.97
35	1.417	2.000	2.814	3.946	5.516	7.686	10.677	14.785	20.414	28.102	38.575	52.800	72.069	98.100	133.176	180.314	243.503	327.997	440.701	590.668	789.747	1053.40	1401.78	1861.05	2465.19	3258.14	4296.65	5653.91	7424.03	9727.86
A-2, PVIF
	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%	11%	12%	13%	14%	15%	16%	17%	18%	19%	20%	21%	22%	23%	24%	25%	26%	27%	28%	29%	30%
1	0.990	0.980	0.971	0.962	0.952	0.943	0.935	0.926	0.917	0.909	0.901	0.893	0.885	0.877	0.870	0.862	0.855	0.847	0.840	0.833	0.826	0.820	0.813	0.806	0.800	0.794	0.787	0.781	0.775	0.769
2	0.980	0.961	0.943	0.925	0.907	0.890	0.873	0.857	0.842	0.826	0.812	0.797	0.783	0.769	0.756	0.743	0.731	0.718	0.706	0.694	0.683	0.672	0.661	0.650	0.640	0.630	0.620	0.610	0.601	0.592
3	0.971	0.942	0.915	0.889	0.864	0.840	0.816	0.794	0.772	0.751	0.731	0.712	0.693	0.675	0.658	0.641	0.624	0.609	0.593	0.579	0.564	0.551	0.537	0.524	0.512	0.500	0.488	0.477	0.466	0.455
4	0.961	0.924	0.888	0.855	0.823	0.792	0.763	0.735	0.708	0.683	0.659	0.636	0.613	0.592	0.572	0.552	0.534	0.516	0.499	0.482	0.467	0.451	0.437	0.423	0.410	0.397	0.384	0.373	0.361	0.350
5	0.951	0.906	0.863	0.822	0.784	0.747	0.713	0.681	0.650	0.621	0.593	0.567	0.543	0.519	0.497	0.476	0.456	0.437	0.419	0.402	0.386	0.370	0.355	0.341	0.328	0.315	0.303	0.291	0.280	0.269
6	0.942	0.888	0.837	0.790	0.746	0.705	0.666	0.630	0.596	0.564	0.535	0.507	0.480	0.456	0.432	0.410	0.390	0.370	0.352	0.335	0.319	0.303	0.289	0.275	0.262	0.250	0.238	0.227	0.217	0.207
7	0.933	0.871	0.813	0.760	0.711	0.665	0.623	0.583	0.547	0.513	0.482	0.452	0.425	0.400	0.376	0.354	0.333	0.314	0.296	0.279	0.263	0.249	0.235	0.222	0.210	0.198	0.188	0.178	0.168	0.159
8	0.923	0.853	0.789	0.731	0.677	0.627	0.582	0.540	0.502	0.467	0.434	0.404	0.376	0.351	0.327	0.305	0.285	0.266	0.249	0.233	0.218	0.204	0.191	0.179	0.168	0.157	0.148	0.139	0.130	0.123
9	0.914	0.837	0.766	0.703	0.645	0.592	0.544	0.500	0.460	0.424	0.391	0.361	0.333	0.308	0.284	0.263	0.243	0.225	0.209	0.194	0.180	0.167	0.155	0.144	0.134	0.125	0.116	0.108	0.101	0.094
10	0.905	0.820	0.744	0.676	0.614	0.558	0.508	0.463	0.422	0.386	0.352	0.322	0.295	0.270	0.247	0.227	0.208	0.191	0.176	0.162	0.149	0.137	0.126	0.116	0.107	0.099	0.092	0.085	0.078	0.073
11	0.896	0.804	0.722	0.650	0.585	0.527	0.475	0.429	0.388	0.350	0.317	0.287	0.261	0.237	0.215	0.195	0.178	0.162	0.148	0.135	0.123	0.112	0.103	0.094	0.086	0.079	0.072	0.066	0.061	0.056
12	0.887	0.788	0.701	0.625	0.557	0.497	0.444	0.397	0.356	0.319	0.286	0.257	0.231	0.208	0.187	0.168	0.152	0.137	0.124	0.112	0.102	0.092	0.083	0.076	0.069	0.062	0.057	0.052	0.047	0.043
13	0.879	0.773	0.681	0.601	0.530	0.469	0.415	0.368	0.326	0.290	0.258	0.229	0.204	0.182	0.163	0.145	0.130	0.116	0.104	0.093	0.084	0.075	0.068	0.061	0.055	0.050	0.045	0.040	0.037	0.033
14	0.870	0.758	0.661	0.577	0.505	0.442	0.388	0.340	0.299	0.263	0.232	0.205	0.181	0.160	0.141	0.125	0.111	0.099	0.088	0.078	0.069	0.062	0.055	0.049	0.044	0.039	0.035	0.032	0.028	0.025
15	0.861	0.743	0.642	0.555	0.481	0.417	0.362	0.315	0.275	0.239	0.209	0.183	0.160	0.140	0.123	0.108	0.095	0.084	0.074	0.065	0.057	0.051	0.045	0.040	0.035	0.031	0.028	0.025	0.022	0.020
16	0.853	0.728	0.623	0.534	0.458	0.394	0.339	0.292	0.252	0.218	0.188	0.163	0.141	0.123	0.107	0.093	0.081	0.071	0.062	0.054	0.047	0.042	0.036	0.032	0.028	0.025	0.022	0.019	0.017	0.015
17	0.844	0.714	0.605	0.513	0.436	0.371	0.317	0.270	0.231	0.198	0.170	0.146	0.125	0.108	0.093	0.080	0.069	0.060	0.052	0.045	0.039	0.034	0.030	0.026	0.023	0.020	0.017	0.015	0.013	0.012
18	0.836	0.700	0.587	0.494	0.416	0.350	0.296	0.250	0.212	0.180	0.153	0.130	0.111	0.095	0.081	0.069	0.059	0.051	0.044	0.038	0.032	0.028	0.024	0.021	0.018	0.016	0.014	0.012	0.010	0.009
19	0.828	0.686	0.570	0.475	0.396	0.331	0.277	0.232	0.194	0.164	0.138	0.116	0.098	0.083	0.070	0.060	0.051	0.043	0.037	0.031	0.027	0.023	0.020	0.017	0.014	0.012	0.011	0.009	0.008	0.007
20	0.820	0.673	0.554	0.456	0.377	0.312	0.258	0.215	0.178	0.149	0.124	0.104	0.087	0.073	0.061	0.051	0.043	0.037	0.031	0.026	0.022	0.019	0.016	0.014	0.012	0.010	0.008	0.007	0.006	0.005
21	0.811	0.660	0.538	0.439	0.359	0.294	0.242	0.199	0.164	0.135	0.112	0.093	0.077	0.064	0.053	0.044	0.037	0.031	0.026	0.022	0.018	0.015	0.013	0.011	0.009	0.008	0.007	0.006	0.005	0.004
22	0.803	0.647	0.522	0.422	0.342	0.278	0.226	0.184	0.150	0.123	0.101	0.083	0.068	0.056	0.046	0.038	0.032	0.026	0.022	0.018	0.015	0.013	0.011	0.009	0.007	0.006	0.005	0.004	0.004	0.003
23	0.795	0.634	0.507	0.406	0.326	0.262	0.211	0.170	0.138	0.112	0.091	0.074	0.060	0.049	0.040	0.033	0.027	0.022	0.018	0.015	0.012	0.010	0.009	0.007	0.006	0.005	0.004	0.003	0.003	0.002
24	0.788	0.622	0.492	0.390	0.310	0.247	0.197	0.158	0.126	0.102	0.082	0.066	0.053	0.043	0.035	0.028	0.023	0.019	0.015	0.013	0.010	0.008	0.007	0.006	0.005	0.004	0.003	0.003	0.002	0.002
25	0.780	0.610	0.478	0.375	0.295	0.233	0.184	0.146	0.116	0.092	0.074	0.059	0.047	0.038	0.030	0.024	0.020	0.016	0.013	0.010	0.009	0.007	0.006	0.005	0.004	0.003	0.003	0.002	0.002	0.001
26	0.772	0.598	0.464	0.361	0.281	0.220	0.172	0.135	0.106	0.084	0.066	0.053	0.042	0.033	0.026	0.021	0.017	0.014	0.011	0.009	0.007	0.006	0.005	0.004	0.003	0.002	0.002	0.002	0.001	0.001
27	0.764	0.586	0.450	0.347	0.268	0.207	0.161	0.125	0.098	0.076	0.060	0.047	0.037	0.029	0.023	0.018	0.014	0.011	0.009	0.007	0.006	0.005	0.004	0.003	0.002	0.002	0.002	0.001	0.001	0.001
28	0.757	0.574	0.437	0.333	0.255	0.196	0.150	0.116	0.090	0.069	0.054	0.042	0.033	0.026	0.020	0.016	0.012	0.010	0.008	0.006	0.005	0.004	0.003	0.002	0.002	0.002	0.001	0.001	0.001	0.001
29	0.749	0.563	0.424	0.321	0.243	0.185	0.141	0.107	0.082	0.063	0.048	0.037	0.029	0.022	0.017	0.014	0.011	0.008	0.006	0.005	0.004	0.003	0.002	0.002	0.002	0.001	0.001	0.001	0.001	0.000
30	0.742	0.552	0.412	0.308	0.231	0.174	0.131	0.099	0.075	0.057	0.044	0.033	0.026	0.020	0.015	0.012	0.009	0.007	0.005	0.004	0.003	0.003	0.002	0.002	0.001	0.001	0.001	0.001	0.000	0.000
31	0.735	0.541	0.400	0.296	0.220	0.164	0.123	0.092	0.069	0.052	0.039	0.030	0.023	0.017	0.013	0.010	0.008	0.006	0.005	0.004	0.003	0.002	0.002	0.001	0.001	0.001	0.001	0.000	0.000	0.000
32	0.727	0.531	0.388	0.285	0.210	0.155	0.115	0.085	0.063	0.047	0.035	0.027	0.020	0.015	0.011	0.009	0.007	0.005	0.004	0.003	0.002	0.002	0.001	0.001	0.001	0.001	0.000	0.000	0.000	0.000
33	0.720	0.520	0.377	0.274	0.200	0.146	0.107	0.079	0.058	0.043	0.032	0.024	0.018	0.013	0.010	0.007	0.006	0.004	0.003	0.002	0.002	0.001	0.001	0.001	0.001	0.000	0.000	0.000	0.000	0.000
34	0.713	0.510	0.366	0.264	0.190	0.138	0.100	0.073	0.053	0.039	0.029	0.021	0.016	0.012	0.009	0.006	0.005	0.004	0.003	0.002	0.002	0.001	0.001	0.001	0.001	0.000	0.000	0.000	0.000	0.000
35	0.706	0.500	0.355	0.253	0.181	0.130	0.094	0.068	0.049	0.036	0.026	0.019	0.014	0.010	0.008	0.006	0.004	0.003	0.002	0.002	0.001	0.001	0.001	0.001	0.000	0.000	0.000	0.000	0.000	0.000

A-3 A-4

	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%	11%	12%	13%	14%	15%	16%	17%	18%	19%	20%	21%	22%	23%	24%	25%	26%	27%	28%	29%	30%
A-3, FVIFA
Periods
1	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2	2.010	2.020	2.030	2.040	2.050	2.060	2.070	2.080	2.090	2.100	2.110	2.120	2.130	2.140	2.150	2.160	2.170	2.180	2.190	2.200	2.210	2.220	2.230	2.240	2.250	2.260	2.270	2.280	2.290	2.300
3	3.030	3.060	3.091	3.122	3.153	3.184	3.215	3.246	3.278	3.310	3.342	3.374	3.407	3.440	3.473	3.506	3.539	3.572	3.606	3.640	3.674	3.708	3.743	3.778	3.813	3.848	3.883	3.918	3.954	3.990
4	4.060	4.122	4.184	4.246	4.310	4.375	4.440	4.506	4.573	4.641	4.710	4.779	4.850	4.921	4.993	5.066	5.141	5.215	5.291	5.368	5.446	5.524	5.604	5.684	5.766	5.848	5.931	6.016	6.101	6.187
5	5.101	5.204	5.309	5.416	5.526	5.637	5.751	5.867	5.985	6.105	6.228	6.353	6.480	6.610	6.742	6.877	7.014	7.154	7.297	7.442	7.589	7.740	7.893	8.048	8.207	8.368	8.533	8.700	8.870	9.043
6	6.152	6.308	6.468	6.633	6.802	6.975	7.153	7.336	7.523	7.716	7.913	8.115	8.323	8.536	8.754	8.977	9.207	9.442	9.683	9.930	10.183	10.442	10.708	10.980	11.259	11.544	11.837	12.136	12.442	12.756
7	7.214	7.434	7.662	7.898	8.142	8.394	8.654	8.923	9.200	9.487	9.783	10.089	10.405	10.730	11.067	11.414	11.772	12.142	12.523	12.916	13.321	13.740	14.171	14.615	15.073	15.546	16.032	16.534	17.051	17.583
8	8.286	8.583	8.892	9.214	9.549	9.897	10.260	10.637	11.028	11.436	11.859	12.300	12.757	13.233	13.727	14.240	14.773	15.327	15.902	16.499	17.119	17.762	18.430	19.123	19.842	20.588	21.361	22.163	22.995	23.858
9	9.369	9.755	10.159	10.583	11.027	11.491	11.978	12.488	13.021	13.579	14.164	14.776	15.416	16.085	16.786	17.519	18.285	19.086	19.923	20.799	21.714	22.670	23.669	24.712	25.802	26.940	28.129	29.369	30.664	32.015
10	10.462	10.950	11.464	12.006	12.578	13.181	13.816	14.487	15.193	15.937	16.722	17.549	18.420	19.337	20.304	21.321	22.393	23.521	24.709	25.959	27.274	28.657	30.113	31.643	33.253	34.945	36.723	38.593	40.556	42.619
11	11.567	12.169	12.808	13.486	14.207	14.972	15.784	16.645	17.560	18.531	19.561	20.655	21.814	23.045	24.349	25.733	27.200	28.755	30.404	32.150	34.001	35.962	38.039	40.238	42.566	45.031	47.639	50.398	53.318	56.405
12	12.683	13.412	14.192	15.026	15.917	16.870	17.888	18.977	20.141	21.384	22.713	24.133	25.650	27.271	29.002	30.850	32.824	34.931	37.180	39.581	42.142	44.874	47.788	50.895	54.208	57.739	61.501	65.510	69.780	74.327
13	13.809	14.680	15.618	16.627	17.713	18.882	20.141	21.495	22.953	24.523	26.212	28.029	29.985	32.089	34.352	36.786	39.404	42.219	45.244	48.497	51.991	55.746	59.779	64.110	68.760	73.751	79.107	84.853	91.016	97.625
14	14.947	15.974	17.086	18.292	19.599	21.015	22.550	24.215	26.019	27.975	30.095	32.393	34.883	37.581	40.505	43.672	47.103	50.818	54.841	59.196	63.909	69.010	74.528	80.496	86.949	93.926	101.465	109.612	118.411	127.913
15	16.097	17.293	18.599	20.024	21.579	23.276	25.129	27.152	29.361	31.772	34.405	37.280	40.417	43.842	47.580	51.660	56.110	60.965	66.261	72.035	78.330	85.192	92.669	100.815	109.687	119.347	129.861	141.303	153.750	167.286
16	17.258	18.639	20.157	21.825	23.657	25.673	27.888	30.324	33.003	35.950	39.190	42.753	46.672	50.980	55.717	60.925	66.649	72.939	79.850	87.442	95.780	104.935	114.983	126.011	138.109	151.377	165.924	181.868	199.337	218.472
17	18.430	20.012	21.762	23.698	25.840	28.213	30.840	33.750	36.974	40.545	44.501	48.884	53.739	59.118	65.075	71.673	78.979	87.068	96.022	105.931	116.894	129.020	142.430	157.253	173.636	191.735	211.723	233.791	258.145	285.014
18	19.615	21.412	23.414	25.645	28.132	30.906	33.999	37.450	41.301	45.599	50.396	55.750	61.725	68.394	75.836	84.141	93.406	103.740	115.266	128.117	142.441	158.405	176.188	195.994	218.045	242.585	269.888	300.252	334.007	371.518
19	20.811	22.841	25.117	27.671	30.539	33.760	37.379	41.446	46.018	51.159	56.939	63.440	70.749	78.969	88.212	98.603	110.285	123.414	138.166	154.740	173.354	194.254	217.712	244.033	273.556	306.658	343.758	385.323	431.870	483.973
20	22.019	24.297	26.870	29.778	33.066	36.786	40.995	45.762	51.160	57.275	64.203	72.052	80.947	91.025	102.444	115.380	130.033	146.628	165.418	186.688	210.758	237.989	268.785	303.601	342.945	387.389	437.573	494.213	558.112	630.165
21	23.239	25.783	28.676	31.969	35.719	39.993	44.865	50.423	56.765	64.002	72.265	81.699	92.470	104.768	118.810	134.841	153.139	174.021	197.847	225.026	256.018	291.347	331.606	377.465	429.681	489.110	556.717	633.593	720.964	820.215
22	24.472	27.299	30.537	34.248	38.505	43.392	49.006	55.457	62.873	71.403	81.214	92.503	105.491	120.436	137.632	157.415	180.172	206.345	236.438	271.031	310.781	356.443	408.875	469.056	538.101	617.278	708.031	811.999	931.044	1067.280
23	25.716	28.845	32.453	36.618	41.430	46.996	53.436	60.893	69.532	79.543	91.148	104.603	120.205	138.297	159.276	183.601	211.801	244.49	282.36	326.24	377.05	435.86	503.92	582.63	673.63	778.77	900.20	1040.36	1202.05	1388.46
24	26.973	30.422	34.426	39.083	44.502	50.816	58.177	66.765	76.790	88.497	102.174	118.155	136.831	158.659	184.168	213.978	248.808	289.49	337.01	392.48	457.22	532.75	620.82	723.46	843.03	982.25	1144.25	1332.66	1551.64	1806.00
25	28.243	32.030	36.459	41.646	47.727	54.865	63.249	73.106	84.701	98.347	114.413	133.334	155.620	181.871	212.793	249.214	292.105	342.60	402.04	471.98	554.24	650.96	764.61	898.09	1054.79	1238.64	1454.20	1706.80	2002.62	2348.80
26	29.526	33.671	38.553	44.312	51.113	59.156	68.676	79.954	93.324	109.182	127.999	150.334	176.850	208.333	245.712	290.088	342.763	405.27	479.43	567.38	671.63	795.17	941.46	1114.63	1319.49	1561.68	1847.84	2185.71	2584.37	3054.44
27	30.821	35.344	40.710	47.084	54.669	63.706	74.484	87.351	102.723	121.100	143.079	169.374	200.841	238.499	283.569	337.502	402.032	479.22	571.52	681.85	813.68	971.10	1159.00	1383.15	1650.36	1968.72	2347.75	2798.71	3334.84	3971.78
28	32.129	37.051	42.931	49.968	58.403	68.528	80.698	95.339	112.968	134.210	159.817	190.699	227.950	272.889	327.104	392.503	471.378	566.48	681.11	819.22	985.55	1185.74	1426.57	1716.10	2063.95	2481.59	2982.64	3583.34	4302.95	5164.31
29	33.450	38.792	45.219	52.966	62.323	73.640	87.347	103.966	124.135	148.631	178.397	214.583	258.583	312.094	377.170	456.303	552.512	669.45	811.52	984.07	1193.51	1447.61	1755.68	2128.96	2580.94	3127.80	3788.96	4587.68	5551.80	6714.60
30	34.785	40.568	47.575	56.085	66.439	79.058	94.461	113.283	136.308	164.494	199.021	241.333	293.199	356.787	434.745	530.312	647.439	790.95	966.71	1181.88	1445.15	1767.08	2160.49	2640.92	3227.17	3942.03	4812.98	5873.23	7162.82	8729.99
31	36.133	42.379	50.003	59.328	70.761	84.802	102.073	123.346	149.575	181.943	221.913	271.293	332.315	407.737	500.957	616.162	758.504	934.32	1151.39	1419.26	1749.63	2156.84	2658.40	3275.74	4034.97	4967.95	6113.48	7518.74	9241.04	11349.98
32	37.494	44.227	52.503	62.701	75.299	90.890	110.218	134.214	164.037	201.138	247.324	304.848	376.516	465.820	577.100	715.747	888.449	1103.50	1371.15	1704.11	2118.06	2632.34	3270.84	4062.91	5044.71	6260.62	7765.12	9624.98	11921.95	14755.98
33	38.869	46.112	55.078	66.210	80.064	97.343	118.933	145.951	179.800	222.252	275.529	342.429	426.463	532.035	664.666	831.267	1040.49	1303.13	1632.67	2045.93	2563.85	3212.46	4024.13	5039.01	6306.89	7889.4	9862.7	12321.0	15380.31	19183.77
34	40.258	48.034	57.730	69.858	85.067	104.184	128.259	158.627	196.982	245.477	306.837	384.521	482.903	607.520	765.365	965.270	1218.37	1538.69	1943.88	2456.12	3103.25	3920.20	4950.68	6249.38	7884.61	9941.6	12526.6	15771.8	19841.60	24939.90
35	41.660	49.994	60.462	73.652	90.320	111.435	138.237	172.317	215.711	271.024	341.590	431.663	546.681	693.573	881.170	1120.71	1426.49	1816.65	2314.21	2948.34	3755.94	4783.64	6090.33	7750.23	9856.76	12527.4	15909.8	20189.0	25596.66	32422.87
A-4, PVIFA
	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%	11%	12%	13%	14%	15%	16%	17%	18%	19%	20%	21%	22%	23%	24%	25%	26%	27%	28%	29%	30%
1	0.990	0.980	0.971	0.962	0.952	0.943	0.935	0.926	0.917	0.909	0.901	0.893	0.885	0.877	0.870	0.862	0.855	0.847	0.840	0.833	0.826	0.820	0.813	0.806	0.800	0.794	0.787	0.781	0.775	0.769
2	1.970	1.942	1.913	1.886	1.859	1.833	1.808	1.783	1.759	1.736	1.713	1.690	1.668	1.647	1.626	1.605	1.585	1.566	1.547	1.528	1.509	1.492	1.474	1.457	1.440	1.424	1.407	1.392	1.376	1.361
3	2.941	2.884	2.829	2.775	2.723	2.673	2.624	2.577	2.531	2.487	2.444	2.402	2.361	2.322	2.283	2.246	2.210	2.174	2.140	2.106	2.074	2.042	2.011	1.981	1.952	1.923	1.896	1.868	1.842	1.816
4	3.902	3.808	3.717	3.630	3.546	3.465	3.387	3.312	3.240	3.170	3.102	3.037	2.974	2.914	2.855	2.798	2.743	2.690	2.639	2.589	2.540	2.494	2.448	2.404	2.362	2.320	2.280	2.241	2.203	2.166
5	4.853	4.713	4.580	4.452	4.329	4.212	4.100	3.993	3.890	3.791	3.696	3.605	3.517	3.433	3.352	3.274	3.199	3.127	3.058	2.991	2.926	2.864	2.803	2.745	2.689	2.635	2.583	2.532	2.483	2.436
6	5.795	5.601	5.417	5.242	5.076	4.917	4.767	4.623	4.486	4.355	4.231	4.111	3.998	3.889	3.784	3.685	3.589	3.498	3.410	3.326	3.245	3.167	3.092	3.020	2.951	2.885	2.821	2.759	2.700	2.643
7	6.728	6.472	6.230	6.002	5.786	5.582	5.389	5.206	5.033	4.868	4.712	4.564	4.423	4.288	4.160	4.039	3.922	3.812	3.706	3.605	3.508	3.416	3.327	3.242	3.161	3.083	3.009	2.937	2.868	2.802
8	7.652	7.325	7.020	6.733	6.463	6.210	5.971	5.747	5.535	5.335	5.146	4.968	4.799	4.639	4.487	4.344	4.207	4.078	3.954	3.837	3.726	3.619	3.518	3.421	3.329	3.241	3.156	3.076	2.999	2.925
9	8.566	8.162	7.786	7.435	7.108	6.802	6.515	6.247	5.995	5.759	5.537	5.328	5.132	4.946	4.772	4.607	4.451	4.303	4.163	4.031	3.905	3.786	3.673	3.566	3.463	3.366	3.273	3.184	3.100	3.019
10	9.471	8.983	8.530	8.111	7.722	7.360	7.024	6.710	6.418	6.145	5.889	5.650	5.426	5.216	5.019	4.833	4.659	4.494	4.339	4.192	4.054	3.923	3.799	3.682	3.571	3.465	3.364	3.269	3.178	3.092
11	10.368	9.787	9.253	8.760	8.306	7.887	7.499	7.139	6.805	6.495	6.207	5.938	5.687	5.453	5.234	5.029	4.836	4.656	4.486	4.327	4.177	4.035	3.902	3.776	3.656	3.543	3.437	3.335	3.239	3.147
12	11.255	10.575	9.954	9.385	8.863	8.384	7.943	7.536	7.161	6.814	6.492	6.194	5.918	5.660	5.421	5.197	4.988	4.793	4.611	4.439	4.278	4.127	3.985	3.851	3.725	3.606	3.493	3.387	3.286	3.190
13	12.134	11.348	10.635	9.986	9.394	8.853	8.358	7.904	7.487	7.103	6.750	6.424	6.122	5.842	5.583	5.342	5.118	4.910	4.715	4.533	4.362	4.203	4.053	3.912	3.780	3.656	3.538	3.427	3.322	3.223
14	13.004	12.106	11.296	10.563	9.899	9.295	8.745	8.244	7.786	7.367	6.982	6.628	6.302	6.002	5.724	5.468	5.229	5.008	4.802	4.611	4.432	4.265	4.108	3.962	3.824	3.695	3.573	3.459	3.351	3.249
15	13.865	12.849	11.938	11.118	10.380	9.712	9.108	8.559	8.061	7.606	7.191	6.811	6.462	6.142	5.847	5.575	5.324	5.092	4.876	4.675	4.489	4.315	4.153	4.001	3.859	3.726	3.601	3.483	3.373	3.268
16	14.718	13.578	12.561	11.652	10.838	10.106	9.447	8.851	8.313	7.824	7.379	6.974	6.604	6.265	5.954	5.668	5.405	5.162	4.938	4.730	4.536	4.357	4.189	4.033	3.887	3.751	3.623	3.503	3.390	3.283
17	15.562	14.292	13.166	12.166	11.274	10.477	9.763	9.122	8.544	8.022	7.549	7.120	6.729	6.373	6.047	5.749	5.475	5.222	4.990	4.775	4.576	4.391	4.219	4.059	3.910	3.771	3.640	3.518	3.403	3.295
18	16.398	14.992	13.754	12.659	11.690	10.828	10.059	9.372	8.756	8.201	7.702	7.250	6.840	6.467	6.128	5.818	5.534	5.273	5.033	4.812	4.608	4.419	4.243	4.080	3.928	3.786	3.654	3.529	3.413	3.304
19	17.226	15.678	14.324	13.134	12.085	11.158	10.336	9.604	8.950	8.365	7.839	7.366	6.938	6.550	6.198	5.877	5.584	5.316	5.070	4.843	4.635	4.442	4.263	4.097	3.942	3.799	3.664	3.539	3.421	3.311
20	18.046	16.351	14.877	13.590	12.462	11.470	10.594	9.818	9.129	8.514	7.963	7.469	7.025	6.623	6.259	5.929	5.628	5.353	5.101	4.870	4.657	4.460	4.279	4.110	3.954	3.808	3.673	3.546	3.427	3.316
21	18.857	17.011	15.415	14.029	12.821	11.764	10.836	10.017	9.292	8.649	8.075	7.562	7.102	6.687	6.312	5.973	5.665	5.384	5.127	4.891	4.675	4.476	4.292	4.121	3.963	3.816	3.679	3.551	3.432	3.320
22	19.660	17.658	15.937	14.451	13.163	12.042	11.061	10.201	9.442	8.772	8.176	7.645	7.170	6.743	6.359	6.011	5.696	5.410	5.149	4.909	4.690	4.488	4.302	4.130	3.970	3.822	3.684	3.556	3.436	3.323
23	20.456	18.292	16.444	14.857	13.489	12.303	11.272	10.371	9.580	8.883	8.266	7.718	7.230	6.792	6.399	6.044	5.723	5.432	5.167	4.925	4.703	4.499	4.311	4.137	3.976	3.827	3.689	3.559	3.438	3.325
24	21.243	18.914	16.936	15.247	13.799	12.550	11.469	10.529	9.707	8.985	8.348	7.784	7.283	6.835	6.434	6.073	5.746	5.451	5.182	4.937	4.713	4.507	4.318	4.143	3.981	3.831	3.692	3.562	3.441	3.327
25	22.023	19.523	17.413	15.622	14.094	12.783	11.654	10.675	9.823	9.077	8.422	7.843	7.330	6.873	6.464	6.097	5.766	5.467	5.195	4.948	4.721	4.514	4.323	4.147	3.985	3.834	3.694	3.564	3.442	3.329
26	22.795	20.121	17.877	15.983	14.375	13.003	11.826	10.810	9.929	9.161	8.488	7.896	7.372	6.906	6.491	6.118	5.783	5.480	5.206	4.956	4.728	4.520	4.328	4.151	3.988	3.837	3.696	3.566	3.444	3.330
27	23.560	20.707	18.327	16.330	14.643	13.211	11.987	10.935	10.027	9.237	8.548	7.943	7.409	6.935	6.514	6.136	5.798	5.492	5.215	4.964	4.734	4.524	4.332	4.154	3.990	3.839	3.698	3.567	3.445	3.331
28	24.316	21.281	18.764	16.663	14.898	13.406	12.137	11.051	10.116	9.307	8.602	7.984	7.441	6.961	6.534	6.152	5.810	5.502	5.223	4.970	4.739	4.528	4.335	4.157	3.992	3.840	3.699	3.568	3.446	3.331
29	25.066	21.844	19.188	16.984	15.141	13.591	12.278	11.158	10.198	9.370	8.650	8.022	7.470	6.983	6.551	6.166	5.820	5.510	5.229	4.975	4.743	4.531	4.337	4.159	3.994	3.841	3.700	3.569	3.446	3.332
30	25.808	22.396	19.600	17.292	15.372	13.765	12.409	11.258	10.274	9.427	8.694	8.055	7.496	7.003	6.566	6.177	5.829	5.517	5.235	4.979	4.746	4.534	4.339	4.160	3.995	3.842	3.701	3.569	3.447	3.332
31	26.542	22.938	20.000	17.588	15.593	13.929	12.532	11.350	10.343	9.479	8.733	8.085	7.518	7.020	6.579	6.187	5.837	5.523	5.239	4.982	4.749	4.536	4.341	4.161	3.996	3.843	3.701	3.570	3.447	3.332
32	27.270	23.468	20.389	17.874	15.803	14.084	12.647	11.435	10.406	9.526	8.769	8.112	7.538	7.035	6.591	6.196	5.844	5.528	5.243	4.985	4.751	4.538	4.342	4.162	3.997	3.844	3.702	3.570	3.447	3.333
33	27.990	23.989	20.766	18.148	16.003	14.230	12.754	11.514	10.464	9.569	8.801	8.135	7.556	7.048	6.600	6.203	5.849	5.532	5.246	4.988	4.753	4.539	4.343	4.163	3.997	3.844	3.702	3.570	3.448	3.333
34	28.703	24.499	21.132	18.411	16.193	14.368	12.854	11.587	10.518	9.609	8.829	8.157	7.572	7.060	6.609	6.210	5.854	5.536	5.249	4.990	4.755	4.540	4.344	4.164	3.998	3.845	3.703	3.571	3.448	3.333
35	29.409	24.999	21.487	18.665	16.374	14.498	12.948	11.655	10.567	9.644	8.855	8.176	7.586	7.070	6.617	6.215	5.858	5.539	5.251	4.992	4.756	4.541	4.345	4.164	3.998	3.845	3.703	3.571	3.448	3.333

IOS Graph

15.00%	A
14.50%		B								Yes
14.00%				C
13.50%
13.00%								D
12.50%
12.00%									E
11.50%
11.00%												F
10.50%
10.00%													G
9.50%											No
9.00%
8.50%
8.00%
7.50%
7.00%
6.50%
6.00%
5.50%
5.00%
4.50%
4.00%
3.50%
0
							600				1000
				Investment Opportunity Schedule
			Project	Expected IRR	Cost	Cumulative			WACC	Money Raised
			A	15.0%	100,000	100,000	Yes		9.75%	$0-$600,000
			B	14.5%	200,000	300,000	Yes		10.50%	$600,000-$1,000,000
			C	14.0%	400,000	700,000	Yes		11.50%	>$1,000,000
			D	13.0%	100,000	800,000	Yes
			E	12.0%	300,000	1,100,000	Yes
			F	11.0%	200,000	1,300,000	No
			G	10.0%	100,000	1,400,000	No

Supply of Funds for Bonds

Bonds
	Yield
											Lower risk brings lower interest rates for you.
									S1		If your perceived default risk falls, you will have more money available to you
											at the same or the same money available at lower rates.
	16
										S2
	10
											Current Yield = annual rate of interest/market price of bond
											$ 600	$ 150	25.0%
											$ 800	$ 150	18.8%
											$ 1,000	$ 150	15.0%
											$ 1,200	$ 150	12.5%
		10	20	30	40	50	60	70	80
							Quantity of funding (millions)

Corporate and Personal Taxation

Tax Structure
	From	To	Bracket Rate	Base Tax	Added Tax	Income Examples	Tax	Weekly Income	Average Tax Rate	Marginal Tax Rate
Corporate	$0	$50,000	15.0%	$0		$40,000	$6,000	$ 961.54	15.00%	15%
	$50,001	$75,000	25.0%	$7,500	+ 0.25 x Income Exceeding 50001	$70,000	$12,500	$ 1,442.31	17.86%	25%
	$75,001	$100,000	34.0%	$13,750	+ 0.34 x Income Exceeding 75001	$85,000	$17,149	$ 1,923.08	20.18%	34%
	$100,001	$335,000	39.0%	$22,249	+ 0.39 x Income Exceeding 100001	$250,000	$80,749	$ 6,442.31	32.30%	39%
	$335,001	$10,000,000	34.0%	$113,899	+ 0.34 x Income Exceeding 335001	$400,000	$135,999	$ 192,307.69	34.00%	34%
	$10,000,001	$15,000,000	35.0%	$3,399,999	+ 0.35 x Income Exceeding 10000001	$10,200,000	$3,469,998	$ 288,461.54	34.02%	35%
	$15,000,001	$18,333,333	38.0%	$5,149,998	+ 0.38 x Income Exceeding 15000001
	$18,333,334	Infinity	35.0%	$6,416,664	+ 0.35 x Income Exceeding 18333334
Single	$0	$2,650	0.0%	$0			$0	$ 50.96
	$2,650	$9,800	10.0%	$0	+ 0.1 x Income Exceeding 2650	$5,000	$235	$ 188.46
	$9,800	$31,500	15.0%	$715	+ 0.15 x Income Exceeding 9800	$10,000	$745	$ 605.77
	$31,500	$69,750	25.0%	$3,970	+ 0.25 x Income Exceeding 31500	$35,000	$4,845	$ 1,341.35
	$69,750	$151,950	28.0%	$13,533	+ 0.28 x Income Exceeding 69750	$75,000	$15,003	$ 2,922.12
	$151,950	$328,250	33.0%	$36,549	+ 0.33 x Income Exceeding 151950	$170,000	$42,505	$ 6,312.50
	$328,250	$999,999	35.0%	$94,728	+ 0.35 x Income Exceeding 328250	$350,000	$102,340	$ 19,230.75
Married	$0	$6,450	0.0%	$0			$0	$ 124.04
	$6,450	$18,450	10.0%	$0	+ 0.1 x Income Exceeding 6450	$9,000	$255	$ 354.81
	$18,450	$51,550	15.0%	$1,200	+ 0.15 x Income Exceeding 18450	$25,000	$2,183	$ 991.35
	$51,550	$109,700	27.0%	$6,165	+ 0.27 x Income Exceeding 51550	$75,000	$12,497	$ 2,109.62
	$109,700	$176,800	30.0%	$21,866	+ 0.3 x Income Exceeding 109700	$150,000	$33,956	$ 3,400.00
	$176,800	$311,900	35.0%	$41,996	+ 0.35 x Income Exceeding 176800	$200,000	$50,116	$ 5,998.08
	$311,900	$999,999	38.6%	$89,281	+ 0.386 x Income Exceeding 311900	$350,000	$103,987	$ 19,230.75

Corn & Rent Supply & Demand

The Price of Corn
	Price				Recall that an increase in costs shifts the supply curve left (or upward).
	5								S2
										S1
	4
	3
	2
	1
									D1
									Demand
		1	2	3	4	5	6	7
										Quanity Demanded
	Price	$ 5	$ 4	$ 3	$ 2	$ 1
	Quantity Demanded	1	2	3	4	5

Supply & Demand Land

Supply and Demand of Land
						Supply of Land
	Price
	5
	4
	3
	2
									D2
	1
									D1
									Demand
		1	2	3	4	5	6	7
										Quanity Demanded and Supplied
	Price	$ 5	$ 4	$ 3	$ 2	$ 1
	Quantity Demanded	1	2	3	4	5

Test Two Tally

Multiple Choice	186
Short-term Costs	126
Hiring Decision	18
Marinal Factor Cost	20
Total	350

Lorenz Curve

Lorenz Curve
		-Area of the Parabola divided by the area of the right Tirangle=Gini Coefficient.
		-The larger the Gini Coefficient, the greater the inequity
% of Wealth
			The degree of Inequality
	% of Population or People