Economic Questions (Calculation Based)

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TECON 480 – Class 4

August 5, 2019

Part 2 - Formulating the cost-benefit model

• Assignment #1 answer key posted on Canvas

• Feedback will be provided ASAP

• Assignment #2 due date will be pushed back from Aug 9

• I will update the assignment due dates tonight

• Instructions available on Canvas

Announcements / Reminders

Last Class

• Discussed the philosophical basis for cost-benefit analysis

• Provided justification for using net social benefits as a

decision-making criterion

• Discussed some limitations of using net benefits as decision-

making criterion

Today’s Class

• Begin a review (?) of microeconomic concepts that are the

foundation of CBA

� Necessary to properly classify and quantity the costs and

benefits used in Steps 3-5

• Discussion of Assignment #1

• Introduction to Assignment #2

Today’s Class

• Microeconomic concepts that are the foundation of CBA:

• Demand curve � willingness to pay

• Supply curve � opportunity cost

• Measuring and interpreting surplus:

• Consumers, producers, government

Introduction to Microeconomics

• CBA is based primarily on microeconomic concepts

• i.e. TECON 200

• These notes are based on Chapter 3 in Boardman

� Measurement of costs and benefits

� Welfare economics

• For simplicity, we assume the presence of perfect competition

throughout this discussion 6

Demand Curves

• A demand curve indicates the quantity of a good that a

person is willing to purchase at various prices

• The market demand curve is the horizontal sum of all

“individual” demand curves in the market

Demand Curves

• The market inverse demand curve represents the price as a

function of the quantity

• Classic graph of demand used in microeconomics

• Prices on the vertical axis

• Quantities on the horizontal axis

• The price can be interpreted as the maximum price that

someone is willing to pay for an additional unit of the good

• The inverse demand curve slopes downward

• Each unit of the good is valued slightly less than the preceding

unit � diminishing marginal utility

Demand Curves

• The highest WTP in society for the first unit of good X is P1

• The highest WTP in society for the second unit of good X is P2

• etc…

• Each additional unit is valued at the value given by the height

of the inverse demand curve at the quantity of interest

� For a given quantity Z, the sum of these WTP values for units

(1, 2, …, Z) represents the WTP of society for these Z units of the

good 10

Demand Curves

• In CBA, benefits generally measured in terms of WTP

� P1 measures the marginal benefit of the first unit

� P2 measures the marginal benefit of the second unit, etc.

• If X* is the quantity consumed, the sum of all marginal

benefits for units (1, 2, …, X*) is the total benefits (B)

� The light and dark grey shaded areas (combined)

Consumer Surplus

• To consume X*, consumers must pay P* for each unit of the

good

• They spend P*X* in total

• price times quantity (the dark grey shaded area)

• The Consumer Surplus (CS) or the “net benefit” to consumers

equals the total benefits received minus the amount paid:

CS = B - P*X*

� CS is represented on the graph by the light grey shaded area

Consumer Surplus

• Changes in consumer surplus is a reasonable measure of the

benefits to consumers from a new project or a new policy

� Consumer surplus provides accurate approximations of WTP

that can be used for CBA

Consumer Surplus

• Assume that the initial price and quantity are P* and X* for

good X

• Then consider a policy that reduces the price of the good X

from P* to P1

� Consumers are better off

�Their consumer surplus has increased exactly by the light and

dark grey area on the next slide’s graph 14

Consumer Surplus

• Light grey shaded area = additional surplus of existing consumers

• Dark grey shaded area = total surplus of new consumers

What is the maximum amount that consumers would be willing to pay

to obtain the price decrease from P* to P1 � the change in consumer surplus

Consumer Surplus

• Change in price

Let Δ� = �1 − �* < 0 (i.e. the price decreases)

• Change in quantity of good X consumed

Let Δ� = �1 − �* > 0 (i.e. the quantity increases)

Consumer Surplus

• If the inverse demand curve is linear, the change in consumer

surplus Δ�� can be computed as:

Δ�� = −(Δ�)�* − ½(Δ�)(Δ�)

� Area of the light grey rectangle + area of the dark grey triangle

• This formula is also valid for a price increase

Consumer Surplus

The price elasticity of demand, � � :

• The percentage change in quantity demanded resulting from a

1 percent increase in the price of the good:

P X E

X P

∆ =

∆

Consumer Surplus

• Price elasticities very useful when we do not know the

demand curve � which is essentially all of the time…

• � �

is always negative, but often presented as its absolute

value (easier to interpret)

� The larger the absolute value of � � , the more elastic

(responsive) is the quantity demanded (i.e. the more sensitive

consumers are to changes in price)

Consumer Surplus

• Given the initial price P* and quantity X*, and using Δ� and Δ�

as the changes in quantity and prices:

• Then, we can rewrite this expression as:

P X E

X P

∆ ≈

∆

d E X P

X P

∆ ∆ ≈

Consumer Surplus

• When substituting this last expression in the changes in

consumer surplus we have:

� If you know the elasticity, you can predict the effect of a price

increase on consumer surplus without knowing the demand curve 21

( )

( ) ( )

CS P X X P

E X P P X

  ∆ = − ∆ − ∆ ∆ 

 

∆ ≈ − ∆ −

Example of CS calculation

• How would you determine the change in consumer surplus due

to decreasing the fare of public transit from $3 to $2?

Taxes

• Taxation is the main source of financing when the government

implements a policy (or a project)

• Suppose that the government imposes a sales tax on the good X

� The price would increase from P* to P2

� Each unit sold is taxed by (P2 - P*)

• Let’s see the graph representing this situation 23

Taxes

• Quantity sold decreases from X* to X2

• Light grey rectangle is the tax revenue generated

• Tax revenue is a transfer from individuals to the government

Taxes

• Dark grey triangle is the deadweight loss (DWL)

• The DWL is the cost of the tax to society

• The DWL is the part of the preceding consumer surplus that is

lost and not offset by any new benefit in the society

• The DWL exists because some of the units previously are no

longer consumed: (X* - X2) units are “lost”

Taxes

• The deadweight loss resulting from the implementation of tax

is given by:

• The DWL is the second part of the Δ�� expression that

represents the area of the dark grey triangle

• Since Δ� represents the tax, we can replace it by �:

( ) 2*

* 2

d E X P

DWL P

∆ ∆ =

* 2

d E X t

DWL P

∆ =

Taxes

• A DWL always* results from the implementation of a tax

• To measure the relative weight of the DWL we use the

“leakage”, the ratio of the DWL to the tax revenue collected:

• If the change in output is small, leakage can be expressed as:

( )* *2 1 d E t

Leakage XP X

= ∆+

* 2

d E t

Leakage P

* almost always…

Assignment #1

• Discussion of answer key

• Environmental benefits: lower emissions / carbon footprint

• Reduced congestion

• Faster commute (dedicated lane + off-board fare collection)

• “Real time” travel information

• Higher transit vehicle capacity

• Fewer accidents (injuries, fatalities)

• Create jobs

• Improved accessibility for individuals with disabilities

• Less frequent stops (faster travel time)

• Work/study on commute (access to wi-fi, lower stress)

• Larger customer base for downtown Tacoma businesses

• Direct connection from rural area to downtown

Potential Benefits?

Tip: try to avoid “double counting” benefits

• Burden on taxpayers

• Possible gas price increases

• Less frequent stops (longer access/egress time)

• Construction infrastructure cost

• Maintenance costs

• Construction duration & delays

• Implementation of traffic signal technology

• Lane limitations on traffic

• Legal risks

• Security

• Fare collection / hiring fare inspectors (capital / labor costs)

• Parking

• Interfering with existing routes

Potential Costs?

Tip: try to avoid “double counting” costs

Supply Curves

• In CBA, we always consider the opportunity costs of resources

• An individual firm usually has a short-run U-shaped marginal

cost (MC) curve

• All costs are opportunity costs

• Short run: at least one factor of production cannot vary

• Example of fixed input: capital 31

Supply Curves

• MC indicates the additional cost to produce each additional

unit of good

• The area below the market supply curve represents the total

variable cost of producing a given amount of good

Supply Curves

• The MC curve intersects the average variable cost (AVC) curve

of the firm exactly at its minimum point

• The segment of a firm’s marginal cost curve above the average

variable cost curve is its supply curve

• Supply curve: the quantity of output the firm will produce at

any given price

• When the price is below the average variable cost, the firm

shuts down because it cannot cover the variable costs 33

Supply Curves

• At price P*, the firm

will produce X*

• By producing more

the firm would lose

money because the

additional units cost

more than the

market price P*

Market Supply Curve

• The market supply curve is the horizontal sum of all “individual”

firms’ supply curves in the market

• Indicates total quantity available on the market at any given price

Market Supply Curve

• The area below the market supply curve represents the total

variable cost of producing a given amount of the good

• Can also interpret it as the minimum revenue required to produce

this amount of the good

Market Supply Curve

• At price P1, firms in the market are willing to supply X1 units

• P1 is also the MC of the X1 th unit

• That’s the quantity that (perfectly competitive) firms want to

supply at this price

Producer Surplus

• Assuming the market price is P*, then firms would supply X*

units

� Firms’ revenue is P*X*

• Revenue = (price per unit) * (quantity sold)

� The light and dark grey shaded areas on the preceding graph

Producer Surplus

• The total variable cost to produce X* is represented by the

dark grey shaded area

• The producer surplus (PS) equals firms’ revenue minus the

total variable cost

PS = P*X* - TVC

• PS is represented on the graph by the light grey shaded area

� PS measures the firms’ benefit 39

Interlude: Bus Rapid Transit

https://www.youtube.com/watch?v=0NHlOwJza54

Social Surplus

• Society’s surplus accounts for the surplus of both consumers

and producers

• Social surplus (SS): �� = �� + ��

• Note: this relationship only holds in the absence of impacts on

the government (i.e. no tax revenue)

� Can find SS in the supply and demand framework

Social Surplus

• This framework incorporates both the supply and demand

curves

• Equilibrium occurs at price P* and quantity X*

• CS = dark grey area

• PS = light grey area

• SS is the sum of both grey areas

� Also find the perfect competition equilibrium rule: P = MC 43

Social Surplus

• How can we find the net social benefits from the basic

microeconomic framework?

• Total consumer benefits are represented by the area below the

demand curve

• Total producer costs are represented by the area below the

supply curve

� Social net benefits equal total consumer benefits minus total

producer costs

• Social net benefits = the dark and light grey areas

Social Surplus

• Demand curve represents marginal benefits (MB)

• Supply curve represents marginal costs (MC)

� Competitive equilibrium is reached when they are equal

� Therefore net social benefits are maximized

• There is no potential gain in increasing production

• The marginal costs would be larger than the marginal benefits 45

Is there a potential gain by decreasing production in this case?

Social Surplus

• In perfect competition, net social benefits and social surplus

are maximized

� This equilibrium is Pareto efficient

• There is no way to increases the benefits of one group without

negatively affecting the benefits of another group

• i.e., it is “allocatively efficient”

• Therefore, a governmental intervention cannot improve the

efficiency in this framework

• In fact, any intervention would create a DWL

Profits

• The producer surplus (PS), as we defined it, does not account for

any fixed costs:

PS = P*X* - TVC

• But, in practice, most projects involve changes in fixed costs that

we need to take into account

Profits

• If there are fixed costs, need to adapt the measurement of the

� Include the fixed cost (FC)

� Profit, π = P*X* - TVC – FC = PS - FC

Profits

• Consequently, social surplus can be rewritten:

�� = �� + �

• A change in policy would result in net social benefits

measured by:

Δ�� = Δ�� + Δ�

Government Surplus

• Sometimes the government intervenes in the economy

• How do we deal with this?

� We need to define a government surplus

• Governmental surplus (GS): financial inflows from taxes minus

governmental expenditures

Government Surplus

• When GS ≠ 0, must rewrite the social surplus as:

�� = �� + �� + �

• A change in policy would result in net social benefits

measured by:

Δ�� = Δ�� + Δ�� + Δ �

� In a competitive market, the net social benefit of a project

equals the change in consumer surplus plus the change in

producer surplus plus the net change in government revenue

Exercise #1

• Assume that the government builds rent-free housing for low-

income residents at cost C

• It provides an increase in consumer surplus of B

• C includes construction and operating costs

• Assume also that there is no change in producer surplus

What are the net social benefits in that case?

Exercise #1

• What if the tenants pay a rent R?

• It is a mistake to include it in the GS

� A rent paid is a transfer from consumers to the government

� It must be ignored in the calculation of net social benefits

• Therefore, this does not change the outcome from that of the

preceding exercise

Exercise #1

• An alternative approach is to consider the gross benefits to

consumers and the social cost to society

• The gross benefits equal the whole area under the inverse

demand curve � Δ�� +

• The total costs to society are the rents plus the construction

and operating cost � + �

Exercise #1

• Therefore, the net social benefits equal:

�� = (Δ�� + ) − (R + �) = Δ�� − � = B − C

� There are often different ways to calculate the net social

benefits

� However, the results are the same (if done properly)

Exercise #2

• Assume now that the government wants to ensure producers

receive a price PT , which is larger than the equilibrium price P*

• At the same time, the government wants to ensure the

producers sell all the output XT that they are willing to supply at

price PT • However, consumers are willing to pay less for this quantity: PD < PT

• PD is the market price without governmental intervention

• We often see this kind of policy (“price supports”) in the

agricultural sector

• Consider a graph representing this situation

Exercise #2

• What can the government do to make sure producers receive

PT for each of the XT units?

Exercise #2

• Suppose the government offers a subsidy of PT – PD

• What are the distributional implications of this policy?

• What happens with the surplus in this situation?

• Δ CS?

• Δ PS?

• Δ GS? 58

Exercise #2

• Consumer surplus:

• Producer surplus:

* 0

before

after D

after before D

CS abP

CS aeP

CS CS CS P beP

∆ = − = >

Consumers are better

off with the policy

* 0

before

after T

after before T

PS P bc

PS P dc

PS PS PS P dbP

∆ = − = >

Producers are better

off with the policy

Exercise #2

• Government surplus:

• Do the gains to consumers and producers outweigh the cost to

the government for this policy?

before

after T D

after before T D

GS P deP

GS GS GS P deP

= −

∆ = − = − <

“Government” is worse

off with the policy

Exercise #2

• What is the social surplus without this policy?

• What is the social surplus with this policy?

� DWL is the area bde

� Society is worse off with the policy

Practice Problem: Part 1

• Demand curve: P = 10,000 – 10Q

• Supply curve: P = 1,000 + 5Q

Question: In equilibrium, calculate the following:

• Consumer surplus = ?

• Producer surplus = ?

• Social surplus = ? 62

Practice Problem: Part 2

• Suppose that the government imposes a tax of 1500 per unit that the producers must pay

Question: In equilibrium, calculate the following:

• Consumer surplus = ?

• Producer surplus = ?

• Government surplus = ?

• Social surplus = ? 63

Practice Problem: Part 3

• What is the deadweight loss of this tax?

• How would we decide whether this tax is a “good” economic

policy?

Assignment #2

• Instructions are posted on Canvas

• Due date will be extended