Problem 1: Ali inherits $10,000 from his great-great aunt in 2008. His great-
great aunt's will require that Ali spend the money before December 31, 2009.
He has two spending options: He can spend the amount either in 2008 or in
2009. Suppose this is Ali's only source of income and the interest rate on loans
or savings is 10 percent.
(a) How much could Ali spend in 2008 if he only consumes in 2008? How
much could Ali spend in 2009 if he only consumes in 2009?
In 2008
$10,000 of the interest rate
$10,000*10/100=$1000 interest rate*1year
Amount he spends=$10,000-1000
$9,000
In 2009
$10,000 of interest rate*2 years
$10,000*10/100*2
Interest=$2,000
Amount he spends=$10,000-2000
$8,000
(b) What is the opportunity cost of consuming $1.00 in 2008 in terms of
forgone consumption in 2009? Draw Ali's budget constraint and optimal
consumption bundle, considering that the spending in 2008 is measured along
the horizontal axis.
If Ali consumes $1 in 2008, it would be advantageous for him because he would not be
charged a big interest rate for example, in 2008, he would be charged an interest of $0.1
while he consumes $1 in 2009, and he would be liable of $ 0.2 interest.
Ali’s Budget constraint curve
(c) Ali decides to spend $6,000 in 2008 and $4,400 in 2009. Show this optimal
consumption bundle using a budget constraint and indifference curve
diagram.
Ali’s indifference curve
Compensated
budget
Problem 2 (10 Points–Theoretical – Paragraph Form): Suppose Sam and
Kevin can produce pens and pencils as shown in the table below.
Pens Pencils
Sam 12
hours
8 hours
Kevin 4 hours 6 hours
(a) Who has a comparative advantage in producing pens? Who has a
comparative advantage in producing pencils?
Kevin has comparative advantage in producing pen since he can only take 4 hours
and also, he has a competitive advantage in producing Pencils since he can only take
6 hours in producing pencils compared to his main competitor Sam who takes 12
hours in production of Pens and 8 hours in production of Pencils. This makes Kevin
to create more time for more production of the two commodities hence making him
have more competitive advantage.
(b) Suppose Sam and Kevin have to each give Flip, a common friend, 10
pens and 10 pencils. Is there a trade that will make both of them better
off? If a trade that would make both of them better off exists, describe
such a trade. If there is no such trade that would make both of them
better off, explain why.
The best trade that both can involve in is the trade of specialization. Each one of
them should specialize on the product they can produce maximally for example,
Kevin should specialize in production of pens since he takes very few hours and
leave the production of pencils to Sam because their time margin in production of
pencils is not such big. This would make them better off since they shall not be
competing for consumers and they shall try to produce the best quality of their
products due to specialization, as specialization makes people, firms and even
organizations produce one best product since it is the only product.
Problem 3 (10 Points - Calculation): If demand is represented by Qd = 50 -
0.5P + 0.005I where I = $50,000 and supply is represented by Qs = 100 + 0.4P
-2W where wages (W) = $15.00, compute the equilibrium price and quantity.
What happens if income falls to I = $40,000?
Qd=50-0.5p+0.005i and I=$50,000
and
Qs=100+0.4p-2w and w=$15.00
Qd
Qd=50-0.5p+ (0.005*50,000)
Qd=50-0.5p+250
Qd=300-0.5p……… (I)
Qs
Qs=100+0.4p-2w
Qs=100+0.4p-(2*15)
Qs=100+0.4p-30
Qs=100+0.4p-30
Qs=70+0.4p……. (ii)
Since Qd=Qs at the equilibrium; then,
300-0.5p=70+0.4p
230/0.9=0.9p/0.9
P=$256
Qd=50-0.5(256) +0.005(50,000)
Qd=50-128+250=172 units
Qs=100+0.4(256)-(2*15)
Qs= (100+102.4)-30
Qs=172.4
Qs=172 units
When income (I) reduces to ($40,000)
Qd=50-0.5(256) +0.005(40,000)
Qd=50-128+200
Qd=122 units
Therefore, when the income (I) falls to ($40,000), the quantity demanded (Qd), will reduce
from 172 units to 122 units.
Problem 4 (10 Points - Calculation): Always Round Tire finds that their
demand curve is P = 50 − .02 Q (note: Marginal Revenue has twice the slope
as the demand curve). What price and quantity combination will maximize
the firm's revenue? What are the total revenue and price elasticity at this
point?
P=50-0.02Q
ΔP/ΔQ=0
P=50-0.02Q/2^2
50/0.01=0.01Q/0.01
Q=5,000
P=50-(0.02*5,000)
P=$100
TR=P*Q
TR=$100*5000
TR=$500,000
Price elasticity= (% Δ in Quantity)/ (%Δ in price)
Pe=5,000/500,000*100
Pe=1,000 units
Problem 5 (10 Points): You are given the following information: (a) Your
firm’s demand equation is defined as follows:
Qd=100−4PA+2Ps+.1 I
, where
Qd
is the quantity demanded for your product,
PA
is the price that you
charge for your product,
Ps
is the price that a competitor charges for a
substitute product, and I is the income for your consumers. You have a
current estimate for all of the variables (at the present levels): (a)
Qd
: 160,
(b)
PA
: $20.00, (c)
Ps
: $20.00, and (d) I: $1,000. Answer the following
questions:
(a) Calculate the elasticity of demand with respect to changes in your price.
Comment on what this result implies (one to two sentences will suffice).
Demand elasticity= (% Δ in Quantity)/ (% Δ in price)
{(4*20) – (20)/20}*100
PE=100 units
(b) Calculate the elasticity of demand with respect to changes in your
competitor’s price. Comment on what this result implies (one to two sentences
will suffice).
{((2*20)-20)/20}*100
PE=100units
(c) Calculate the elasticity of demand with respect to changes in the income of
your consumer. Comment on what this result implies (one to two sentences
will suffice).
(1,000-1,000)/1,000
0/1000
Income elasticity=0 units
Problem 6 (10 Points - Calculation): Always Round Tire is the only producer
of tires for the new British import, the Maxi Copper. Demand for a set of four
tires is P = 800 - 5Q (note: Marginal Revenue has twice the slope as the
demand curve) while the cost incurred by the firm is MC = 15Q. What would
be the monopoly price and quantity? What would happen to price and
quantity if the market was perfectly competitive (assuming the same costs)?
P=800-5Q
0 =800-10Q-15Q
800/25=25Q/25
Q=32 units
P=800-(5*32)
P=800-160=$640
Under perfect competition, the firm would become a price taker and not price
maker .The prices would be lower and closer to the costs since there are many
producers and consumers. The quantity of goods produced increases and is
homogeneous. There will be high level of substitute goods.
Problem 7 (10 Points - Calculation): Cost Analysis – Fill in the following cost
table.
Qua
ntity
Tota
l
Cost
Margin
al Cost
Total
Fixed
Cost
Total
Variable
Cost
Average
Total Cost
Average
Fixed Cost
Average
Variable
Cost
0 100 - 100 0 - - -
1 120 20 100 20 120 1 20
2 138 18 100 38 69 2 19
3 151 13 100 51 50.3 3 17
4 165 11 100 65 15 4 16.3
5 175 10 100 75 35 5 15
6 190 15 100 90 31.7 6 15
7 200 20 100 100 20 7 14.3
8 234 34 100 134 29.3 8 16.8
9 263 29 100 163 29.2 9 18.1
10 296 37 100 196 10 19.6
Problem 8 (20 Points): Given the following demand and supply curves: (a)
Qd=−P+10
and (b)
Qs=P
.
a) Calculate the inverse demand function (provide below) and graph the
two lines on Figure 1 (5 Points).
The inverse of the demand function is the same as the average revenue function.
Qd=-p+10
Qd/-1=-p/-1+10/-1
P=-10-Q
b) Calculate and label the Consumer Surplus and Producer Surplus (5
points).
To calculate the total consumer surplus achieved, we calculate the area of
shaded sky blue color triangle in Fig 2 below Fig 1;
Consumer surplus=1/2*base*height
For this case, our base is equilibrium quantity
(Qm)
Area=1/2*10*1=5units
Consumer surplus=5 units
To calculate producer surplus, calculate the area of the triangle
Labeled producer surplus in Fig 2.This triangle equals our
Consumer surplus triangle. Therefore, producer surplus=5 units
as well.
Fig 1: For perfect competitive
c) Add an additional line for marginal revenue (note that the slope of the
marginal revenue line is twice the demand curve), graph the demand,
perfectively competitive supply, and the marginal revenue line on Figure
2. Identify the following areas on your new figure: (a) deadweight loss to
the economy, (b) consumer surplus, and (c) producer surplus in this new
market environment (10 Points).
Fig 1(b): of Perfect or Pure competition and Figure 2: Monopolies
Not
Allocatively
Efficient:
P >
MC
Pure
Competition
§
Monopolies
Producer
\I~
Surplus
!
N
.
Q
pe
