outline - university of colorado boulderwhere have we come from? part i i consumers have a set of...

Outline

Introduction

E�ciency

Excise Tax

Subsidy

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Where have we come from?Part I

I Consumers have a set of preferences over a basket of goodsI Consumers choose the basket of goods that is a↵ordable and

maximizes their utility

maxX ,Y

U(X ,Y )

s.t. px

X + p

y

Y I

Part II

I Firms are able to transform inputs into output using a givenproduction technology

I They choose the inputs mix that minimizes the cost of makinga given output quantity

minK ,L

wL+ rK

s.t. Q = f (K , L)

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Where have we come from?

Part II, cont.

I Firms are assumed to be price takers

I After optimizing the input mix, the firm chooses the outputquantity which maximizes the firm’s profit.

maxQ

PQ � TC (Q)

I The firm shuts down production if price falls below theshut-down price (unable to cover their non-sunk costs)

I In the short-run, the plant size and number of firms in anindustry is fixed ! upward sloping supply

I In the long-run, firm’s choose optimal plant size and operateat the minimum e�cient scale. Firms can enter/exit theindustry ! zero economic profit

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What’s Next

In this chapter, we look at the e↵ect of government interventionsin a perfectly competitive market.What are the types of government intervention?

IExcise Tax: Tax on a specific commodity (e.g., cigarettes)

ISubsidy: The opposite of an excise tax, the government paysmoney to a firm (consumer) for the production (consumption)of a good (e.g., vaccines)

IPrice ceiling: The government fixes a maximum price for agood (e.g., rent controls)

IQuotas (Production/Import): The government restrictsquantity of a good in the market in order to increase price(e.g., agricultural markets)

ITari↵s: A tax levied specifically on imported goods to restrictgoods coming from other countries

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Introduction

I These policies typically make some people better o↵ and somepeople worse o↵. It is important to understand who are thewinners and losers so you can understand the policy debatesthat take place.

I All of the analysis in this chapter is done as a partial

equilibrium analysis

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Introduction

Partial Equilibrium Analysis: An analysis that studies thedetermination of equilibrium price and output in a single market,taking as given the prices in all other markets.

General Equilibrium Analysis: An analysis that determines theequilibrium prices and quantities in more than one marketsimultaneously

I For example - If apartments are rent controlled, could thisa↵ect the prices in the housing market?

I Changes in one sector often spill over into other sectors

I If airline prices between NYC and Boston ", could this a↵ecttrain prices?

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Another Assumption

No Externalities - add this to the list of assumptions aboutperfectly competitive markets

IExternality: the e↵ect that an action of any decision makerhas on the well-being of another consumer or producer,beyond the e↵ects transmitted by changes in prices

I Example Negative Externality- Pollution produced by a firmnegatively e↵ects your health, but firm doesn’t pay you tocompensate you for this negative e↵ect

I Example Positive Externality - Vaccination, the more peoplewho are vaccinated the less likely you are to get the disease,you aren’t paying those who got vaccinated for the benefitsthat accrue to you

In this, chapter, we will use Consumer Surplus to measureconsumer’s welfare and Producer Surplus to measure producerwelfare

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Economic E�ciency in a Competitive Market - InvisibleHand

A key feature of a Perfectly Competitive Market

I In equilibrium, it allocates resources e�ciently

Note: Requires all of our assumptions from Ch. 9

I Perfect Information (Lemon Problem)

I No one firm/consumer has market power(Monopoly/Monopsony)

I No externalities

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What do we mean by e�cient?

All desired trading has been accomplished

I All benefits from trade have been exhausted (this issue istaken up in more detail in Ch. 16)

I Can’t make someone better o↵ without making someoneworse o↵ (Pareto E�cient)

Let’s take a look at a graph to see why competitive market ise�cient

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E�ciency in Competitive Equilibrium

Q

P

D

$20

S

$2

$8

6

E

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Q

P

D

$20

S

$2

$8

6

E

Competitive Equilibrium:

P

⇤ = 8Q

⇤ = 6At point E

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Q

P

D

$20

S

$2

$8

6

E

What about welfare?

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Q

P

D

$20

S

$2

$8

6

E

What about welfare?Consumer Surplus

(1/2)(20� 8)(6) = $36

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Q

P

D

$20

S

$2

$8

6

E

What about welfare?Consumer Surplus

(1/2)(20� 8)(6) = $36

Producer Surplus

(1/2)(8� 2)(6) = $18

Total Surplus = $36 + $18 = $54

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Q

P

D

$20

S

$2

$8

6

E

4

$12

$6

A

B

What if eq. was 4 million units?

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Q

P

D

$20

S

$2

$8

6

E

4

$12

$6

A

B


- Consumer willing to pay $12

- Producer willing to sell for $6

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Q

P

D

$20

S

$2

$8

6

E

4

$12

$6

A

B




- They should make the trade, and

exchange one more unit

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Q

P

D

$20

S

$2

$8

6

E

4

$12

$6

A

B

Total Surplus could increase by:

Change in Total Surplus

(1/2)(12-6)(2)=$6

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Q

P

D

$20

S

$2

$8

6

E

7

$9

$6

F

G


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Q

P

D

$20

S

$2

$8

6

E

7

$9

$6

F

G




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Q

P

D

$20

S

$2

$8

6

E

7

$9

$6

F

G




- They should not make the trade, and

exchange one less unit

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Q

P

D

$20

S

$2

$8

6

E

7

$9

$6

F

G

Total Surplus could increase by:

Change in Total Surplus

(1/2)(9-6)(1)=$1.5

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Q

P

D

$20

S

$2

$8

6

E

When demand curve is above supply curve:

Total Surplus increases if output rises

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Q

P

D

$20

S

$2

$8

6

E

When demand curve is below supply curve:

Total Surplus increases if output falls

11/29


=) Any production level above/below Q

⇤ = 6 will lead to alower amount of surplus than the competitive equilibrium

I The Invisible Hand: We came to this e�cient allocation by

1. Consumers acting in self-interest to maximize utility2. Producers acting in self-interest to maximize profit

I No one told the consumers and producers how to act, therewas no “social planner”

=) The equilibrium output produced when everyone was actingin their own self-interest is one that maximizes net economicbenefits (Total Surplus) as long as we are in a perfectlycompetitive market

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Excise Tax

What is it?

I Tax on a specific commodity

How does it work?

I Suppose government imposes a $6 per unit tax on gasoline

I Now what consumer pays (Pd) and amount the sellers receive(Ps) di↵ers (“tax wedge”)

P

d = P

s + 6

I More generally: Pd = P

s + T

I Let’s imagine that the seller has the administrativeresponsibility of collecting the tax and giving it to thegovernment

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Equilibrium with an Excise Tax

Q

P

D

$20

S0

$2

$8

6

E

Competitive Equilibrium

S0 + 6

4

$12

M

N

$6

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Q

P

D

$20

S0

$2

$8

6

E

S0 + 6

Supply Shifts " with Tax

4

$12

M

N

$6

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Q

P

D

$20

S0

$2

$8

6

E

S0 + 6

4

$12

M

N

$6

Equilibrium with Tax:

P

d = $12P

s = $6Q = 4

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Q

P

D

$20

S0

$2

$8

6

E

S0 + 6

4

$12

M

N

$6

Let’s see what happens to Welfare

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Q

P

D

$20

S0

$2

$8

6

E

S0 + 6

4

$12

M

N

$6


Consumer Surplus=$12 (-$24)

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Q

P

D

$20

S0

$2

$8

6

E

S0 + 6

4

$12

M

N

$6



Producer Surplus=$8 (-$10)

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Q

P

D

$20

S0

$2

$8

6

E

S0 + 6

4

$12

M

N

$6



Producer Surplus=$8 (-$10)Tax Revenue=$24

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Q

P

D

$20

S0

$2

$8

6

E

S0 + 6

4

$12

M

N

$6



Producer Surplus=$8 (-$10)Tax Revenue=$24Deadweight Loss=$6

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Outcomes - Excise Tax

1. Market underproduces relative to e�cient level (smaller Q)

2. Price the consumer pays increases ($8 ! $12)

3. Price suppliers receive decreases ($8 ! $6)

4. Consumer Surplus and Producer Surplus both fall

5. Some of this decrease is received by the government in theform of tax revenue

6. Some of this decrease is deadweight loss (gains from exchangethat used to happen that is no longer happening)

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Deadweight Loss

Deadweight Loss: A reduction in net economic benefits resultingfrom an ine�cient allocation of resources.

I Exchange that would have taken place that doesn’t due to the“tax wedge” causing a di↵erence in supplier and consumerprice

16/29

Practice: Impact of an Excise Tax

This example is the algebraic version of the graph we justanalyzed. Suppose demand and supply are given as follows:

Q

d = 10� 0.5Pd

Q

s =

(�2 + P

s , P

s � 2

0 P

s < 2

where Q

d is the quantity demanded when the price consumers payis Pd , and Q

s is the quantity supplied when the price producersreceive is Ps .

a) With no tax, what are the equilibrium price and quantity?

b) Suppose the government imposes an excise tax of $6 per unit.What will the new equilibrium quantity be? What price willbuyers pay? What price will sellers receive?

17/29

Incidence of a Tax

Assume a downward sloping demand and upward sloping supplycurve

Incidence of a tax: A measure of the e↵ect of a tax on the priceconsumers pay and sellers receive in the market

I Both Consumers & Sellers are a↵ected no matter who collectsthe tax

I Consumer price paid "I Seller price received #I But - Who shares more of the burden?

I Let’s examine two cases of a $10 tax

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Case1: Incidence of a TaxDemand is Relatively Inelastic Compared with Supply

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Case 2: Incidence of a TaxSupply is Relatively Inelastic Compared with Demand

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Incidence of a Tax

Case 1: Relatively Inelastic Demand

I Consumer price rises a lot: $8

I Producer price decreased just a little: $2

I Why: Consumer’s demand is inelastic so can handle largechanges in price without adjusting quantity by very much

Case 2: Relatively Inelastic Supply

I Consumer price rises a little: $2

I Producer price decreased a lot: $8

I Why: Producer’s supply is inelastic so can handle largechanges in price without adjusting quantity by very much

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Incidence of a Tax

How can we calculate this?

�P

d

�P

s

=✏Q

s ,P

✏Q

d ,P

How the tax a↵ects consumers relative to pro-ducers can be described by the ratio of the priceelasticity of supply to the price elasticity of de-mand

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Example - Incidence of a Tax

Example 1: Suppose ✏Q

s ,P = 0.5, ✏Q

d ,P = �0.5, and a $2 tax islevied. What is the incidence of the tax?

✏Q

s ,P

✏Q

d ,P=

0.5

�0.5= �1 =

�P

d

�P

s

A ratio of 1 means the tax is shared equally between consumersand producers. So, with a $2 tax, the consumer price will " $1 andthe producer price # $1

23/29

Example - Incidence of a Tax

Example 2: Suppose ✏Q

s ,P = 2.0, ✏Q

d ,P = �0.5, and a $2 tax islevied. What is the incidence of the tax?

✏Q

s ,P

✏Q

d ,P=

2

�0.5= �4 =

�P

d

�P

s

The increase of price to consumers is 4x that of producers. So,with a $2 tax, you can get the incidence by dividing tax by 5(2/5=0.4). The consumer price will " $1.60 (0.4 · 4) and theproducer price # $0.40 (0.4 · 1). You could also solve this system ofequations:

�4�P

s = �P

d

�P

d ��P

s = 2

24/29

Incidence of a Tax - Cigarettes

Consider the case of cigarettesI What you think demand is?

I ElasticI Inelastic

I What do you think supply is relative to demand?I ElasticI Inelastic

Who bears more of the burden of a cigarette tax?

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Subsidy

What is it?

I Instead of taxing, government pays each seller a subsidy of $Xper unit

How does it work?

I Now, consumer pays (Pd) and amount the seller receives(Pd + X )

P

s = P

d + X

I How to model this?

TC

NS

= 400 + 2Q + Q

2 =) MC = 2 + 2Q

TC

S

= 400 + 2Q + Q

2 � XQ =) MC = 2 + 2Q � X

Marginal cost curve is reduced (lowers supply curve)

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Equilibrium with a SubsidyX = $3

Q

P

D

$20

S0

$2

$8

6

E

Competitive Equilibrium

S0 � 3

7

$9

R

U

$6

27/29


Q

P

D

$20

S0

$2

$8

6

E

S0 � 3

Supply Shifts # with Subsidy

7

$9

R

U

$6

27/29


Q

P

D

$20

S0

$2

$8

6

E

S0 � 3

7

$9

R

U

$6

Equilibrium with Subsidy:

P

d = $6P

s = $9Q = 7

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Q

P

D

$20

S0

$2

$8

6

E

S0 � 3

7

$9

R

U

$6


27/29


Q

P

D

$20

S0

$2

$8

6

E

S0 � 3

7

$9

R

U

$6


Consumer Surplus=$49 (+$13)

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Q

P

D

$20

S0

$2

$8

6

E

S0 � 3

7

$9

R

U

$6



Producer Surplus=$24.5 (+$6.5)

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Q

P

D

$20

S0

$2

$8

6

E

S0 � 3

7

$9

R

U

$6




Subsidy Cost=$21

27/29


Q

P

D

$20

S0

$2

$8

6

E

S0 � 3

7

$9

R

U

$6




Subsidy Cost=$21

Deadweight Loss=$1.5

27/29

Outcomes - Subsidy

1. Market overproduces relative to e�cient level (larger Q)

2. Price the consumer pays decreases ($8 ! $6)

3. Price suppliers receive increases ($8 ! $9)

4. Consumer Surplus and Producer Surplus both increase

5. The increase is paid for by the government (subsidy cost)

6. However, the subsidy costs more than the total gain inconsumer and producer surplus leading to a deadweight loss

28/29

Practice: Impact of a Subsidy

As before, demand and supply are given by:

Q

d = 10� 0.5Pd

Q

s =

(�2 + P

s , P

s � 2

0 P

s < 2

a) Suppose the government provides a subsidy of $3 per unit.Find the equilibrium quantity, the price buyers pay, and theprice sellers receive.

29/29

outline - university of colorado boulderwhere have we come from? part i i consumers have a set of...

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