Economics 102

Question 1

Suppose the Kingdom of Atlantis decides to levy a tax of one shekel on the production of each widget.

(a) Demonstrate that the decline in consumer and producer surplus resulting from the tax exceeds the amount of tax revenue collected.

(b) Given the tax, what is the relationship between the price paid by consumers and the marginal cost of production?

A Tax and Economic Welfare

S w/o tax

S with tax

P0

P1

P2

Q0Q1

Tax per unit

A

BC D

E

F

G

H

No Tax Tax Change

CS

PS

Tax Revenue

W

The area (DG) is the deadweight loss from the tax

ABCD

EFGH

Zero

ABCDEFGH

A

H

BCEF

ABCEFH

-(BCD)

-(EFG)

-(DG)

BCEF

• The decline in CS and PS is BCDEFG while the level of tax revenue is BCEF

• The price paid by consumers (P1) exceeds the price received by producers (P2) and thus the price that consumers pay exceeds MC

Question 2

• Suppose now that the Kingdom eliminates the tax and decides instead to subsidize the widget industry. Suppose the subsidy equals one shekel for every widget produced.

• (a) Demonstrate that the increase in consumer and producer surplus resulting from the subsidy is less than the amount of money that the government gives the producers.

• (b) Given the subsidy, what is the relationship between the price paid by consumers and the marginal cost of production?

• (c) Given your answers to (1a) , (1b), (2a), and (2b), what is the “optimal” relationship (from society’s overall point of view) between price and marginal cost?

Subsidies and Economic Welfare

S w/ Subsidy

S w/o Subsidy

P2

P1

P3

Q1 Q2

Producer

Consumer

EquilibriumAmount Producers Receive from Government

Net Price with Subsidy

Price Without Subsidy

Price With Subsidy

S w/ Subsidy

S w/o Subsidy

P2

P1

P3

Q1 Q2

Producer

Consumer

Amount Producers Receive from Government

CS

PS

Gov’t EXP

W

Without Subsidy

With Subsidy Change

AB

EH

A

B

EF G

C

D

H

zero

ABEH

ABEFG

BCEH

BCDEFG

ABEH - D

EFG

BC

BCDEFG

-D

AREA “D’ represents the Deadweight loss from thesubsidy

• The increase in CS and PS is BCEFG• The cost of the subsidy program is

BCDEFG which is larger• The price that consumers pay(P2) is less

than the net price that producers receive (P3) and thus the price that consumers pas is less than marginal cost

• The optimal outcome is when the price that consumers pay equals MC

Question 3

• Consider the following cost schedule:

Q 0 1 2 3 4 5 6 7 8 9 10 11

TC 100 122 140 155 175 200 230 265 305 350 400 455

• a) Assume the price of the product is $50. What is the profit maximizing level of output?

• b) What is the lowest price at which the firm will produce? Given this price, how many units should the firm produce? Explain.

• C) What is the break-even price? Given this price, how many units should the firm produce? Explain.

Q 0 1 2 3 4 5 6 7 8 9 10 11

TC 100 122 140 155 175 200 230 265 305 350 400 455

AVC 22 20 18.33 18.75 20 21.67 23.57 25.63 27.78 30 32.27

ATC 122 70 51.67 43.75 40 38.33 37.86 38.13 38.89 40 41.36

MC 22 18 15 20 25 30 35 40 45 50 55

The lowest price at which the firm will operate is the minimum AVC. In this case, thisis 18.33 when Q = 3

The breakeven price is the minimum ATC. In this case, thisis 37.86 when Q = 7

Profits are maximized when p=MC assuming P is greater than or equal to AVC. Thus, when the price is 50, profits are maximized when Q = 10

Question 44) Consider the nation of Atlantis which is populated by rational,

perfectly informed, identical individuals.One of the staples of the diet is fish. To keep it affordable, the price of

fish is regulated below the market equilibrium price.The Parliament of Atlantis is currently considering legislation that would

eliminate the price regulation. According to the Laissez Faire party, the removal of the price control would improve resource allocation. Opponents of the policy change argue that decontrol would reduce the welfare of the typical inhabitant.

Upon hearing of your expertise in economics, the King has requested your advice. Please advise him on this proposed change in policy using the tools of analysis developed in this course.

Assume the maximum legal price is P1

P1

P2

AB

CD

E F

G

PriceControl

DecontrolChange

CS

PS

W

A,C

G

A,C,G

P1

P2

AB

CD

E F

G

PriceControl

DecontrolChange

CS

PS

W

A,C

G

A,C,G

A,B

C,D,G

A,B,C,D,G

P1

P2

AB

CD

E F

G

PriceControl

DecontrolChange

CS

PS

W

A,C

G

A,C,G

A,B

C,D,G

A,B,C,D,G

B-C

C,D

B,D

Question 55) To protect its domestic sneaker industry, the Kingdom of Atlantis

currently disallows imports of sneakers.The Laissez‑Faire party has proposed that the edict be revoked.

Based on the writings of Adam Smith, it is argued that free trade will improve the allocation of resources.

The political party known as the Atlantis-First party opposes the importation of foreign sneakers. They argue that permitting foreign sneakers into Atlantis will enrich foreigners at the expense of the typical Atlantian.

The Laissez-Faire party concedes that removing the edict will hurt the domestic producers of sneakers. Yet, they maintain that Atlantis will be better off, not worse off, if the edict if revoked.

Upon hearing of your expertise in the field of economics, the King has requested your advice. Using the tools of analysis developed in this course, what would you advise the King?

World Price

BanTrade Permitted Change

CS

PS

W

A

B

C D

E

A

B,E

A,B,E

Domestic Supply

Demand

World Price

BanTrade Permitted Change

CS

PS

W

A

B

C D

E

A

B,E

A,B,E

A,B,C,D

E

A,B,C,D,E

Domestic Supply

World Price

BanTrade Permitted Change

CS

PS

W

A

B

C D

E

A

B,E

A,B,E

A,B,C,D

E

A,B,C,D,E

B,C,D

-B

C,D

Domestic Supply

Question 6

• (A) (i) Briefly explain why a price taker can expected to produce at the output level where MC = Price. (ii) How does this output level compare to the point of diminishing marginal returns to labor? (iii) How does this output level compare to the point where ATC is minimized? (iv) Are there any exceptions to this “rule?”

• (B) Why is it in society’s interests for producers to operate at the point where MC = P ?

Δprofit = ΔTR - ΔTC

Divide both sides by the change in output, ΔQ

ΔQ=

ΔQ ΔQ

ΔProfit ΔTR ΔTC

Marginal Profit = MR - MC

Profit = TR - TC

When Firms are price takers

• Marginal Revenue(MR) = Price

Thus,

Marginal Profit = P - MC

The Profit Frontier

Q

Profit

0

The Slope of the Curve is the change in profits whenOutput increases by one unit. In other words, the slopeRepresents Marginal Profit

Marginal Profit is positiveAt this point

Marginal Profit is negativeAt this point

Marginal Profit is zero atThis point

Q*

Profit Maximization when a Firm is a Price Taker

• From the previous slide, it is clear that profit maximization requires that a price taker produce where Marginal Profits equal zero

• But Marginal Profit equals P – MC

• Thus, profit maximization for a price taker requires that a price taker produce where MC = P

How does the profit maximizing level of output compare to the point of diminishing marginal returns to labor?

• MPL is maximized at the point of diminishing marginal returns to labor

• Given the inverse relationship between MPL and MC, this means that MC is minimized at the point of diminishing marginal returns to labor

Suppose Price equals P5 and Q = Qo. Are Profits at a Maximum?

AVC

ATC

MC

Q0

P5

MC@Q0

Note that Price exceeds MCWhen Q = Q0

Thus, marginal profits are positiveat Q0 which means that profits willrise if more is produced

How does the profit maximizing level of output compare to the point of diminishing marginal returns to labor?

Based on the previous slide, the profit maximizing level of output is greaterThan the output level that corresponds to diminishing marginal returns

How does the profit maximizing level of output compare to the point

where ATC is minimized?

Suppose Price equals P5 and Q = Q2. Are Profits at a Maximum?

AVC

ATC

MC

Q2

P5

MC@Q2

Note that Price exceeds MCWhen Q = Q2

Thus, marginal profits are positiveat Q2 which means that profits willrise if more is produced

Q*

In the previous slide, ATC is minimized at Q2. This is less than the output level that maximizes profits

The next slide shows that if P < ATC, then the profit maximizing level of output will be less than the output level that minimizes ATC

Suppose Price equals P4 and Q = Q2. Are Profits at a Maximum?

AVC

ATC

MC

Q2

P4

Q*

Are there any exceptions to the rule of P=MC

• Yes, if P < AVC

• Please see the next slide. In this case, losses are minimized by not producing at all

Suppose P equals P1

AVC

ATC

MC

Q*

P1

ATC@Q*

AVC@Q*

A B

D

TR = E,F

VC =C,D,E,F

PS = -(C,D)

FC =A,BPROFIT = -(A,B,C,D)

C

E

F

Why is it in society’s interests for producers to operate at the point

where MC = P ?

• According to the law of diminishing marginal utility, the utility that consumers receive from a good increases at a diminishing rate

• Based on the law of diminishing marginal returns to labor, the total cost of producing a good can be expected to increase at an increasing rate

Total Utility

Q

U

Total Cost

Q

U

Total Utility vs Total Cost

Q

U

Total Utility vs Total Cost

Q

U

Q*

Please note that Utility minusTC is maximized at Q*

Also note that the slope of theUtility function and the totalCost function are equal at Q*

The equality of the slopes meansThat MU = MC at Q*

If MU = MC, then P = MC

Question 7

Consider the nation of Atlantis which is populated by rational perfectly informed individuals. All markets are competitive and unregulated

Because of reduced supply due to flooding, the price of gasoline has increased sharply.

Using consumer and producer surpluses, what is the effect of the flood on economic welfare when the price of gasoline is unregulated? What happens to the profits of the gasoline producers? Why does this happen?

CS

PS

W

S0

Before AfterChange

A

BC

E FP0

P1

Q0Q1

D

Demand

S1

A,B,C,D

E,F

A,B,C,DE,F

A -(B,C,D)

B,E B-F

A,B,E -(C,D,F)

The change in economic welfareEquals –(CDF) and thus society is worse Off. Observe that producers in thisCase are better off given that areaB is larger than area F.

Question 8A

8) (A) The company known as Mississippi.com has just reported the following financial results.

• Sales $ 14 million• Fixed Costs $ 20 million• Variable Costs $11 million• profit (loss) ($17) million• number of units sold1 million

Given that the firm’s losses exceed its revenues, the firm has been advised to cease production. Before doing so, the CEO of the firm wants your advice. Using the tools of analysis presented in class, what advice would you provide Mississippi ?

Mississipi.com

• The firm has a net loss of 17 million• Based on its fixed costs of 20 million, the firm

would have a loss of 20 million if it closed• Since losing 17 million is preferred to losing 20

million, the firm should stay open in the short run• Observe that this conclusion is the result of total

revenue being larger than variable costs.

Congo.com

• B) The company known as Congo.com has just reported the following financial results.

• Sales$ 14 million• Fixed Costs$ 11 million• Variable Costs $20 million• profit (loss) ($17) million• number of units sold1 million• Given that the firm’s losses exceed its revenues, the firm

has been advised to cease production. Before doing so, the CEO of the firm wants your advice. Using the tools of analysis presented in class, what advice would you provide Congo ?

Congo.com

• The firm has a net loss of 17 million• Based on its fixed costs of 11 million, the firm

would have a loss of 11 million if it closed• Since losing 11 million is preferred to losing 17

million, the firm will minimize it losses by closing • Observe that this conclusion is the result of total

revenue being smaller than variable costs.

9) Consider the country of Atlantis. One of the key industries in the country is the widget industry. Because of its importance, the firm that makes widgets is owned by the government.

The firm currently produces at the point of diminishing marginal returns to labor.

The Laissez Faire party has proposed that the firm be privatized. Is there any merit to this proposal? Explain, using the tools of analysis presented in class.

Price

Q0 Q*

MC

Point where profits areMaximized when theFirm is a price taker.Also the point ofAllocative efficiency