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Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 9 Suggested Solutions Chapter 10

Part A: Multiple Choices 1.

Suppose that the market for cigarettes is initially in equilibrium and is perfectly competitive. The demand curve can be expressed as P  60  Q d ; the supply curve can be expressed as P  0.5Qs . Quantity is expressed in millions of boxes per month. Now suppose that the federal government imposes a production quota on cigarettes of 30 million boxes per month. What is the change in consumer surplus (per million boxes) associated with the quota? A. $450. B. $350. C. $300. D. $50.

2.

Suppose that a market is initially in equilibrium. The initial demand curve is P  90  Qd . The initial supply curve is P  2Qs . Suppose that the government imposes a $3 tax on this market. What is the dead-weight loss due to the tax? A. $3. B. $2. C. $1.50. D. $1.00.

3.

Consider a perfectly competitive market with market supply Qs  2  P and market demand Qd  30  P . What is total surplus in this market? A. 98 B. 128 C. 196 D. 256

4.

Suppose that the market for corn is initially in equilibrium and is perfectly competitive. The demand curve can be expressed as P  10 Q d ; the supply curve can be expressed as s P  0.25Q . Quantity is expressed in millions of bushels. Now suppose that the federal government imposes a price floor of $3 per bushel of corn. What is the new equilibrium quantity traded in this market? A. Q = 8; B. Q = 2; C. Q=7 D. Q=3

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 9 Suggested Solutions Chapter 10

5.

Suppose that the market for cigarettes is initially in equilibrium and is perfectly competitive. The demand curve can be expressed as P  60  Q d ; the supply curve can be expressed as P  0.5Qs . Quantity is expressed in millions of boxes per month. Now suppose that the federal government imposes a production quota on cigarettes of 30 million boxes per month. What is the level of excess supply in this market? A. There is no excess supply. There is an excess demand of Q = 30. B. There is no excess supply or demand. C. There is an excess supply of Q = 30. D. There is an excess supply of Q = 20.

6.

Suppose that a market is initially in equilibrium. The initial demand curve is P  90  Qd . The initial supply curve is P  2Qs . Suppose that the government imposes a $3 tax on this market. What is the change in consumer surplus due to the tax? A. $450. B. $420.50. C. $29.50. D. $0.50.

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 9 Suggested Solutions Chapter 10

Part B: Conceptual Questions 1. What is the significance of the “invisible hand’’ in a competitive market?

In a long-run equilibrium, a competitive market allocates resources efficiently. As Adam Smith wrote over 200 years ago, it is as though there is an “Invisible Hand” guiding a competitive market to the efficient level of production and consumption. This occurs through producers and consumers acting in their own self-interest to maximize profits and utility. 2. Will a price ceiling always increase consumer surplus? Will a price floor always increase producer surplus?

Price ceilings and price floors will not always make consumers and producers better off. In particular, if the price ceiling is set above the equilibrium price or if the price floor is set below the equilibrium price, the price ceilings and floors will have no effect. In addition, depending on which consumers or producers are able to purchase in or supply to the market, consumer surplus or producer surplus may be lower after the imposition of the price ceiling or price floor. 3. Will a production quota in a competitive market always increase producer surplus?

Producer surplus may increase. If the most efficient producers serve the market, producer surplus will increase for some levels of the quota. However, if the quota is too low (for example, close to zero), producer surplus could actually decrease. 4. With a price floor, will the most efficient producers necessarily be the ones supplying the market?

No, it is not clear which producers will supply the market. Because the price is held above the equilibrium price there are many producers who will compete to supply the market, even more than would exist in equilibrium. There is no reason to believe that the most efficient producers will necessarily be the ones supplying the market.

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 9 Suggested Solutions Chapter 10

Part C: Calculations 1. Suppose that the market for cigarettes in Luganville has the following supply and demand curves: QS = P; QD = 50 − P, where the quantities are measured in thousands of units. Suppose that the Luganville Municipal Council needs to raise $300,000 in revenue and decides to do this by taxing the cigarette market. What should the excise tax be in order to raise the required amount of money?  

Suppose that the required tax is $T. Let’s start by writing down what we know.

In equilibrium with the excise tax:

1. 𝑃𝑐 = 𝑃𝑠 + 𝑇 where 𝑃𝑐 is the consumer price and 𝑃 𝑠 is the supplier price. 2. 𝑄 𝑠 = 𝑄𝑑 3. The government revenue = 300,000 = 𝑄 ∗ ∗ 𝑇 where 𝑄∗ is the new equilibrium quantity. Given that we can put quantity supplied and quantity demanded in terms of consumer prices (see additional things we know below) we have three equations and three unknowns. (𝑃𝑐 , 𝑃𝑠 𝑎𝑛𝑑 𝑇) We also know:

4. 𝑄 𝑠 = 𝑃𝑠 5. 𝑄 𝑑 = 50 − 𝑃𝑐 Using equation 2, and substituting in equation 4 and 1 we get:

𝑄 𝑠 = 𝑄𝑑 𝑃 𝑠 = 50 − 𝑃𝑐 𝑃 𝑠 = 50 − (𝑃𝑠 + 𝑇) 2𝑃𝑠 = 50 − 𝑇 𝑃 𝑠 = 25 − 0.5𝑇

Since the equilibrium quantity is 𝑄 𝑠 = 𝑄𝑑 = 𝑃𝑠 , we therefore have: 𝑄 ∗ = 25 − 0.5𝑇

Now we can use equation 3 to determine how the tax is. The Municipal Council needs to raise $300,000, we must have 𝑇𝑄 ∗ = 300,000. Substituting for 𝑄 ∗, we obtain

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 9 Suggested Solutions Chapter 10 300,000 𝑇

= 25 − 0.5𝑇

300,000 = 25𝑇 − 0.5𝑇 2 𝑇 2 − 50𝑇 + 600 = 0 (𝑇 − 20)(𝑇 − 30) = 0 

(Remember that Q is measured in thousands of units)



So we get two possible values for the tax: T = $20 or T = $30. Either one would generate $300,000 in tax revenues, though of course T = $20 would do so with a smaller deadweight loss.

2. Suppose the market for corn in Pulmonia is competitive. No imports and exports are possible. The demand curve is Qd = 10 − Pd, where, Qd is the quantity demanded (in millions of bushels) when the price consumers pay is Pd. The supply curve is

where Qs is the quantity supplied (in millions of bushels) when the price producers receive is Ps.

A. What are the equilibrium price and quantity?

Setting Qd  Qs results in 10  P  4  P P  $7 per bushel

Substituting this result into the demand equation gives Q  3 million bushels. B. At the equilibrium in part (a), what is consumer surplus? producer surplus? deadweight loss? Show all of these graphically. At the equilibrium, consumer surplus is 1 2 (10  7)3  4.5 and producer surplus is 1 (7  4)3  4.5 . There is no deadweight loss in this case and total net benefits equal $9 million. 2

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019

Price

Tutorial 9 Suggested Solutions Chapter 10

16.00 14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00

Supply

Demand A B

0

2

4

6

8

10

Quantity (millions of bushels)

In the graph above, area A represents consumer surplus and area B represents producer surplus.

C. Suppose the government imposes an excise tax of $2 per unit to raise government revenues. What will the new equilibrium quantity be? What price will buyers pay? What price will sellers receive? If the government imposes an excise tax of $2, the new equilibrium will be 10  ( P s  2)  4  P s P  $6 per bushel

Substituting back into the equation for P d yields P d  8 , and substituting P s into the supply equation implies Q  2 million. D. At the equilibrium in part (c), what is consumer surplus? producer surplus? the impact on the government budget (here a positive number, the government tax receipts)? deadweight loss? Show all of these graphically. Now the consumer surplus is 1 2 (10  8)2  2 , the producer surplus is 1 2 (6  4)2  2 , the tax receipts are 2(2)  4, and the deadweight loss is 1 2 (8  6)(3  2)  1 (all measured in millions of dollars).

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019

Price

Tutorial 9 Suggested Solutions Chapter 10

14.00 12.00 Demand 10.00 A 8.00 C 6.00 B 4.00 2.00 0.00 0

Supply + 2

Supply

D E

2

4

6

Quantity (millions of bushels)

In the graph above, area A represents consumer surplus, area B represents producer surplus, areas C+D represent government tax receipts, and area E represents the deadweight loss.

E. Suppose the government has a change of heart about the importance of corn revenues to the happiness of the Pulmonian farmers. The tax is removed, and a subsidy of $1 per unit is granted to corn producers. What will the equilibrium quantity be? What price will the buyer pay? What amount (including the subsidy) will corn farmers receive? If the government provides a subsidy of $1, the new equilibrium will be 10  ( P s 1)  4  P s P s  $7.5 per bushel

Substituting back into the equation for P d yields P d  6.5 , and substituting P s into the supply equation implies Q  3.5 million.

F. At the equilibrium in part (e), what is consumer surplus? producer surplus? What will be the total cost to the government? deadweight loss? Show all of these graphically.

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 9 Suggested Solutions Chapter 10

Price

Now the consumer surplus is 1 2 (10  6.5)3.5  6.125 , the producer surplus is 1 (7.5  4)3.5  6.125 , the subsidy paid is 1(3.5)  3.5 (negative since the government is paying 2 this amount), and the deadweight loss is 1 2 (7.5  6.5)(3.5  3)  0.25 (all measured in millions of dollars). Demand

9.50 8.50 7.50 6.50 5.50 4.50 3.50 2.50

Supply

C A B F

Supply - 1 E

0

0.5

1

1.5

2

2.5

3

D

3.5

4

4.5

5

Quantity (millions of bushels)

In the graph above, areas A+B+E represent consumer surplus, areas B+C+F represent producer surplus, areas B+C+D+E represent the government subsidy payment, and area D represents the deadweight loss.

G. Verify that for your answers to parts (b), (d), and (f) the following sum is always the same: consumer surplus + producer surplus + budgetary impact + deadweight loss. Why is the sum equal in all three cases? For part (b), the sum of consumer surplus, producer surplus, budgetary impact, and deadweight loss is 4.5  4.5  0  0  9 ; for part (d), the sum is 2  2  4  1  9 ; and for part (f) it is 6.125 + 6.125 – 3.5 + 0.25 = 9. (As above, all are measured in millions of dollars.) These sums are all the same because the deadweight loss measures the difference between net benefits (in terms of CS, PS, and budgetary impact) under the competitive outcome and net benefits under a form of government intervention.

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 9 Suggested Solutions Chapter 10

3. In a perfectly competitive market, the market demand curve is given by Qd = 200 − 5Pd, and the market supply curve is given by Qd = 35Ps. A. Find the equilibrium market price and quantity demanded and supplied in the absence of price controls. Pd = Ps = $5; Qd = Qs = 175 units.

B. Suppose a price ceiling of $2 per unit is imposed. What is the quantity supplied with a price ceiling of this magnitude? What is the size of the shortage created by the price ceiling? Qs= 70 units. C. Find the consumer surplus and producer surplus in the absence of a price ceiling. What is the net economic benefit in the absence of the price ceiling?

D. Find the consumer surplus and producer surplus under the price ceiling. Assume that rationing of the scarce good is as efficient as possible. What is the net economic benefit in this case? Does the price ceiling result in a deadweight loss? If so, how much is it? E. Find the consumer surplus and producer surplus under the price ceiling, assuming that the rationing of the scarce good is as inefficient as possible. What is the net economic benefit in this case? Does the price ceiling result in a deadweight loss? If so, how much is it?

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 9 Suggested Solutions Chapter 10

The surplus implications of a price ceiling are shown below.

Consumer surplus

Producer surplus

With No Price Ceiling

With Price Ceiling: Efficient Rationing

Impact of Price Ceiling

A+B+C+I

A+B+F

F–C–I

($3,062.50)

($2,310)

(-$752.50)

G+F+E+H

G

-F-E-H

($437.50)

($70)

(-367.50)

Net benefits (consumer surplus + producer surplus)

A+B+C+I+G+F+E+H A+B+F+G ($3,500) ($2,380)

-C-I-E-H

Deadweight loss

Zero

C+E+I+H ($1,120)

C+E+I+H ($1,120)

With No Price Ceiling

With Price Ceiling: Inefficient Rationing

Impact of Price Ceiling

A+B+C+I

I+H+K+L

H+K+L-A-B-C-

($3,062.50)

($490)

(-$2572.5)

G+F+E+H

G

-F-E-H

($437.50)

($70)

(-367.50)

Consumer surplus

Producer surplus

(-$1,120)

Net benefits (consumer surplus + producer surplus)

A+B+C+I+G+F+E+H I+H+K+L+G ($3,500) ($560)

K+L-A-B-C-F-E

Deadweight loss

Zero

A+B+C+F+E+F -K-L

A+B+C+F+E+F -K-L

($2,940)

($2,940)

(-$2,940)

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 9 Suggested Solutions Chapter 10

P 40

A

C

B

S

I 5 2

H

E

F

J

L

K

D

G 70

120

175 70

190 200

Q...