Economic Questions (Calculation Based)

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TECON 480 – Class 6

August 9, 2019

Part 2 - Formulating the cost-benefit model

• Assignment #2 due Aug 16

• Instructions available on Canvas

Announcements / Reminders

Last Class

• Discussed how to evaluate benefits in the primary market

affected by a policy/project

• When markets are efficient

• When markets are distorted

• Main focus is on the concept of externalities

Today’s Class

• Discuss how to evaluate costs in the primary market affected

by a policy/project

Valuing Inputs: Opportunity Costs

• To implement a project, resources/inputs are required

• Example: building a bridge requires

• Labor

• Materials

• Land

• Equipment

• When resources are devoted to a project, they are not

available for any other purpose

� Have to consider the opportunity cost of the resources 5

• Conceptually, these costs equal the value of the best

alternative use of these resources

• Opportunity costs represented by areas under supply curves

• These areas are the “theoretically appropriate” measure of

the costs of resources

• In practice, the most convenient way to measure this cost is

the direct budgetary outlay needed to purchase the resources

Valuing Inputs: Opportunity Costs

• Depending on circumstances, the direct budgetary outlay can

be close or equal to the theoretical appropriate measure

• When the market for a resource is efficient and purchases of the

resource for the project will have a negligible effect on the price

of the resource

� Opportunity costs will be accurately estimated

• When the market for the resource is efficient, but purchases for

the project will have a noticeable effect on prices

� Opportunity costs will be slightly overstated 7

Valuing Inputs: Opportunity Costs

• When the market for the resource is inefficient, using direct

budgetary outlays would considerably overstate or understate

opportunity costs

� This occurs whenever there is a market failure

• Important: relevant opportunity costs are what must be given

up today and in the future, not what has already been given

� The latter costs are "sunk" costs and should not factor into

the decision-making process 8

Valuing Inputs: Opportunity Costs

Measuring Opportunity Costs: Efficient Markets

• We will consider two cases in efficient markets:

1. Perfectly elastic supply curves

2. Perfectly inelastic supply curves

Perfectly Elastic Supply Curves

• A perfectly elastic supply curve is horizontal

• Represents a market for which the project will not have an

impact on the price of the goods even if the government

consumes it

• Example: pencils

• Assume that the new project requires the purchase of q’ units

of the good

� The demand curve shifts right to reflect this new (higher)

demand 11

Perfectly Elastic Supply Curves

• Because the supply curve is horizontal, the price remains the

same after the demand increase: �0

• Marginal costs of the resource are constant

• �0 is the opportunity cost of an extra unit

• �0 × �′ is the opportunity cost of the project and is represented

by the grey area ab�1�0 on the graph

= the actual amount paid by the government

Perfectly Elastic Supply Curves

• What does this tell us?

Because most inputs have neither steeply rising nor declining

marginal cost curves, it is often reasonable to presume that

expenditures required for project inputs equal their opportunity

costs

• This is the case when:

• Only small amounts of the good are used for a project

• There is no reason to believe there is a relevant market failure 14

Perfectly Elastic Supply Curves

Example for Assignment #2

• How would we measure the gross benefits of an investment in

public transit?

� Step 1: graph the market for transit travel

� Step 2: graph the market for auto travel

“Economic Development”

• https://www.youtube.com/watch?v=8bl19RoR7lc

• A perfectly inelastic supply curve is vertical

• Represents a market in which the total quantity of output is

fixed

• Example: land

• In our example, this quantity will be A

• Any quantity consumed by the government is a quantity that

cannot be used by the private sector 17

Perfectly Inelastic Supply Curves

D: private sector demand curve

S: supply curve of good

• If producers sell the A units to the private sector, their revenue

will be P × A

• Represented by the area ��0

• If the government wants to purchase all A units, it will have to

pay the same price as the private sector, P × A

Perfectly Inelastic Supply Curves

• Suppose the government buys the A units

� The opportunity cost is not only the price paid but also all

benefits that would be created if those units would have been

sold to the private sector

• Consequently, we also have to take into account the consumer

surplus as an opportunity cost

• This consumer surplus is lost if the private sector cannot purchase

the good

• This consumer surplus is represented by the area a��

Perfectly Inelastic Supply Curves

• In this case, the opportunity cost is the area under the

demand curve and to the left of the supply curve: a��0

• Important: this cost is more than the rectangular area below

the price line that was valid for the perfectly elastic case

• Intuition: with perfectly inelastic supply curve, resources are

scarce and opportunities must be foregone if those inputs are

used for something (resources are not ‘scarce’ if supply curve

is perfectly elastic)

Perfectly Inelastic Supply Curves

Measuring Opportunity Costs:

Efficient Markets with Price Effects

• When a project requires the purchase of a large quantity of a resource, the price should increase

• Recall: what happens to the equilibrium price when demand increases and supply is unchanged?

• Therefore, the project faces an upward-sloping supply curve for that resource

• In the following graph, we assume that the government needs q’ units of the good for the project

• D is the private demand for the good

• D + q’ is the total demand for the good, including the government demand

Measuring Opportunity Costs:

Efficient Markets with Price Effects

• The government demand creates a price increase from �0 to �1 in the market

� Private sector reduces its consumption from �0 to �2

�Total consumption increases from �0 to �1

Measuring Opportunity Costs:

Efficient Markets with Price Effects

• The q' units of the resource purchased for the project come

from two distinct sources:

1. Units bid away from their previous buyers

2. Additional units sold in the market

• The cost of the resource for the project is �1 × �′

� represented by the rectangular area B+C+E+F+G 25

Measuring Opportunity Costs:

Efficient Markets with Price Effects

• When computing the opportunity cost, also need to take into

account all changes in consumer and producer surplus

� Therefore, have to understand the impact of the government

behavior on consumers and producers

� What is the effect of this price increase on CS and PS? 26

Measuring Opportunity Costs:

Efficient Markets with Price Effects

Producer surplus:

• Producers sell more units at a higher price

• Change in PS is positive and measured by the area A+B+C

Consumer surplus:

• Consumers buy fewer units at a higher price

• Change in CS is negative and measured by the area A+B 27

Measuring Opportunity Costs:

Efficient Markets with Price Effects

• Gain in PS > loss in CS

� Net gain in private surplus = A+B+C-(A+B) = C

• Therefore, the opportunity cost is:

Opportunity cost = cost of the resources - net gain in private surplus

= (B+C+E+F+G) - C = B+E+F+G

• Area C is a transfer from consumers to producers

Measuring Opportunity Costs:

Efficient Markets with Price Effects

• Important: when prices change, budgetary outlays do not

equal social costs

• However, unless the price rise is significant, the net gain in

private surplus will be small relative to total budgetary costs

• In such a case, budgetary outlays give a good approximation of

the opportunity cost

• If prices do increase substantially, the budgetary costs must be

adjusted to reflect this gain 29

Measuring Opportunity Costs:

Efficient Markets with Price Effects

• If demand and supply curves are linear (or approximately

linear), the net gain in private surplus is given by

• The opportunity cost can be found by computing the

difference between the cost of the resources and the net gain

in private surplus

� Therefore, the opportunity cost is given by

Measuring Opportunity Costs:

Efficient Markets with Price Effects

( ) 1 0

2 P P q′−

( ) 1 0

2 P P q′+

• The average of the new and old prices is a shadow price:

� Reflects the social opportunity cost of purchasing the

resource more accurately than either the old price or the new

price alone

Measuring Opportunity Costs:

Efficient Markets with Price Effects

( ) 1 0

2 P P+

• Market inefficiencies complicate the estimation of opportunity

costs

• Shadow pricing is needed to accurately measure the opportunity

cost in three common situations:

1. The government purchases an input at a price below its

opportunity cost

2. The government hires labor from a market in which there is

unemployment

3. The government purchases inputs for a project from a monopolist

Measuring Costs: Inefficient Markets

Purchases Below Opportunity Costs

• Example: CBA of the criminal justice system

• Issue: how to measure the cost of jurors in a court?

• They receive a per diem compensation for their time

• These per diem do not reflect the “true value” of the time of the

jurors

• Their value of time is implied by their wage rates

• Budgetary outlay to jurors almost certainly understates the

opportunity cost of jurors’ time

� shadow pricing is necessary

• A better estimate of jurors’ opportunity cost would be to take

into account:

• Their commuting expenses

• Plus the number of juror-hours multiplied by either the average

or median hourly wage rate for the area 34

Purchases Below Opportunity Costs

Labor market with

minimum wage ��

• �: pre-project labor

demand curve

• �′: extra labor demand

due to project

• �� (or � when no

project) workers

demanded at ��

• � workers willing to

work at ��

• � − �� = unemployment 38

Hiring Unemployed Labor

• How to measure the social cost of hiring �′ extra workers for

the project?

• There are at least five possible alternative measures of it

Hiring Unemployed Labor

Measure A: Opportunity costs equal zero

• Considers unemployed time as valueless

• This is inappropriate for two reasons

1. Many unemployed persons are engaged in some valuable

activities

• Examples: job search, childcare, home improvements, etc.

2. Even when completely at leisure, leisure itself is valuable 40

Hiring Unemployed Labor

Measure B: Use the total budgetary expenditure on labor for

the project (�� x ��′)

• Substantially overstates the true social cost

� Part of this area is producer/worker surplus and cannot be

considered as a social cost

• Producer surplus can be seen as a transfer

• This component should be subtracted from the expenditure

• Therefore, this measure is inappropriate

Hiring Unemployed Labor

Measure C: Use the area under the supply curve between �� and �� as the cost estimate

• This is a correction of Measure B

� Subtracting the producer surplus (area �� ) from the

budgetary outlay

• The area �� provides an estimate of the opportunity cost

of the newly hired workers

Hiring Unemployed Labor

Measure D: Refining Measure C

• With Measure C, we made the implicit assumption on the

reservation wage of the workers hired for the project (from � to ��) � reservation wage = height of supply curve

• However, the range could be larger (from � to ��)

• i.e. all those willing to work at wage ��

• Solution: take the average reservation wage

� The social cost of hiring workers for the project would be

equal to

Hiring Unemployed Labor

( ) 1

2 m r P P L′+

Measure E: Solving a problem with Measure D

• In Measure D, the lowest reservation wage � is often unknown

• In this case, use � = 0

• In Practice, this value could be very low

• So, this is not an overly strong assumption

� The social cost of hiring workers for the project would be equal

to 44

Hiring Unemployed Labor

2 m P L′

Purchases from a Monopoly

• The government’s budgetary outlay overstates the social costs

from the purchase

� With monopoly, price > marginal cost of production

• Theoretically, the price should be adjusted downward using

shadow pricing

• In practice, with most markets the error resulting from using

unadjusted budgetary expenditures is often not very large 45

The General Rule

• Other market distortions can also affect opportunity costs:

• When supply is taxed, direct expenditure outlays overestimate

opportunity cost

• When supply is subsidized, expenditures underestimate

opportunity cost

• When supply exhibits positive externalities, expenditures

overestimate opportunity cost

• When supply exhibits negative externalities, expenditures

underestimate opportunity costs

• Rule: “Opportunity cost equals direct expenditures on the

factor minus (plus) gains (losses) in social surplus occurring in

the factor market.” 46

“Jobs are Costs”

Quoting Prof. John Whitehead at http://www.env-econ.net/:

• “The point is not that jobs are bad things, in fact they are

great for households and firms. Households earn income

greater than their opportunity costs and firms earn [revenue]

greater than what they must pay in income (i.e., exchange in

the labor market creates value). But jobs are not the things

you want to count up as a measure of the benefits of

environmental policy. Because as soon as you do government

will start trying to create jobs where the benefits of the jobs

are less than the costs (e.g., bridges to nowhere).”

“Bridge to Nowhere”

The Gravina Island Bridge:

• https://en.wikipedia.org/wiki/Gravina_Island_Bridge

• https://www.youtube.com/watch?v=0AGn6z2ZeIg

Example: Externalities and Surplus Calculations

Suppose the market for auto travel currently has the following:

• Demand: P = 1000 – 10Q

• Marginal private cost: P = 100 + 2Q

• Marginal external cost: P = Q

where P is the monetary value or cost per trip and Q is the

number of trips

Example: Externalities and Surplus Calculations

Determine the following:

• Current level of auto travel, Q =

• Efficient level of auto travel, Q* =

• Deadweight loss = 53

Example: Externalities and Surplus Calculations

Compare 2 possible policies on the deadweight loss in the auto

market:

1. Implementing a tax of 20 per auto trip

2. A subsidy of public transit that causes auto demand to

change to P = 750 – 10Q