EXAM 4 ANSWER KEY
Version A
I. Multiple choice
(1)f. (2)a. (3)b. (4)a. (5)b. (6)a. (7)b.
II. Problems
(1) [Economy-wide efficiency: 12 pts]
- $12 (= marginal cost).
- $5 (= marginal cost).
- Firm B (because it has lower marginal cost).
- 8 million, so that marginal costs are equal.
- 12 million, so that marginal costs are equal.
- $7, because each firm will then maximize its own profit by choosing its output level so that its marginal cost equals this price.
(2) [Economy-wide efficiency: 20 pts]
- 1/3 garments.
- 3 pounds of food.
- $2, because in competitive equilibrium, price equals marginal cost.
- $6, because in competitive equilibrium, prices reflect the slope of the production possibility curve for the economy as a whole: if the opportunity cost of a unit of clothing is 3 units of food, then a unit of clothing must be 3 times as expensive as a unit of food.
- $6, because in competitive equilibrium, price equals marginal cost.
- Ashley's budget line should have intercept at 30 on food axis and intercept of 10 on clothing axis.
- -3.
- 3 pounds of food.
- 1/3 garments.
- 3, because Ashley's preferred bundle is at a tangency between her budget line and the highest indifference curve she can reach, and at a tangency the slope of the indifference curve must equal the slope of the budget line.
(3) [Monopoly, price discrimination: 22 pts]
- Since demand curve is linear, MR curve must have same intercept and twice the slope. So MR curve should have intercept at $13 on price axis, and slope = -1/1 thousand.
- 6 thousand, where MR=MC.
- $10, on demand curve.
- $36 thousand = Rev - TC = price × quantity - AC × quantity.
- $9 thousand.
- $3 thousand.
- 8 thousand, because anyone willing to pay at least the marginal cost will be served.
- $88 thousand, because with every customer paying a different price, revenue = area of the trapezoid under demand curve down to horizontal axis.
- $48 thousand = Rev - TC = Rev - AC × quantity.
- $0, because consumer surplus is defined as willingness-to-pay minus price, but with perfect price discrimination willingness-to-pay equals price for every customer.
- $0, because with perfect price discrimination, everyone willing to pay the marginal cost is served.
(4) [Competition versus collusion: 16 pts]
- 12 billion.
- $7 (= marginal cost).
- $7.
- Since demand curve is linear, MR curve must have same intercept and twice the slope. So MR curve should have intercept at $13 on price axis, and slope = -1/1 billion.
- 8 billion, where MR = MC.
- $5 (= marginal cost).
- $9, on demand curve.
- $8 billion.
(5) [Monopolistic competition: 12 pts]
- Al's demand equation is
P_{A} = P_{B} + 1 - (Q_{A}/1000)
= 2.00 + 1 - (Q_{A}/1000)
= 3 - (Q_{A}/1000).
Al's marginal revenue curve must have same intercept and twice slope:
MR = 3 - 2(Q_{A}/1000).
- Set MR = MC = $2 and solve to get 500 gallons.
- Insert 500 gallons into demand equation to get $2.50.
- Now Al's demand equation is
P_{A} = P_{B} + 1 - (Q_{A}/1000)
= 3.50 + 1 - (Q_{A}/1000) = 4.50 - (Q_{A}/1000).
Al's marginal revenue curve must have same intercept and twice slope:
MR = 4.50 - 2(Q_{A}/1000).
- Set MR = MC = $2 and solve to get 1250 gallons.
- Insert 1250 gallons into demand equation to get $3.25.
- Two points extra credit: Given Al's price P_{A} and Bob's price P_{B}, which customers will choose to buy from Al's Store? To find the dividing point x, set the perceived total prices equal:
P_{A}* = P_{B}*
P_{A} + 0.25 x = P_{B} + 0.25 (4-x).
Solving for x gives
x = 2 (P_{B} - P_{A} + 1).
Now 500 customers per mile live along this road, so the number of customers choosing to buy one gallon of milk from Al's Store is
Q_{A} = 500 x = 1000 (P_{B} - P_{A} + 1).
(6) [Monopoly price discrimation: 8 pts]
- 25 percent.
- 15 percent.
- $15.
- $18.
III. Critical thinking [3 pts]
Fredonia's economy is at point B on the production-possibility curve.
If all markets were competitive, Fredonia would be at the efficient outcome, point C--that is, at the tangency between the production possibility curve and the highest attainable indifference curve of the representative consumer.
However, the market for energy is a monopoly, so the quantity of energy is reduced. Therefore Fredonia is at point B.
Version B
I. Multiple choice
(1)e. (2)b. (3)c. (4)b. (5)d. (6)c. (7)c.
II. Problems
(1) [Economy-wide efficiency: 12 pts]
- $6 (= marginal cost).
- $15 (= marginal cost).
- Firm A (because it has lower marginal cost).
- 10 million, so that marginal costs are equal.
- 6 million, so that marginal costs are equal.
- $8, because each firm will then maximize its own profit by choosing its output level so that its marginal cost equals this price.
(2) [Economy-wide efficiency: 20 pts]
- 1/2 garments.
- 2 pounds of food.
- $2, because in competitive equilibrium, price equals marginal cost.
- $4, because in competitive equilibrium, prices reflect the slope of the production possibility curve for the economy as a whole: if the opportunity cost of a unit of clothing is 2 units of food, then a unit of clothing must be 2 times as expensive as a unit of food.
- $4, because in competitive equilibrium, price equals marginal cost.
- Ashley's budget line should have intercept at 30 on food axis and intercept of 15 on clothing axis.
- -2.
- 2 pounds of food.
- 1/2 garments.
- 2, because Ashley's preferred bundle is at a tangency between her budget line and the highest indifference curve she can reach, and at a tangency the slope of the indifference curve must equal the slope of the budget line.
(3) [Monopoly, price discrimination: 22 pts]
- Since demand curve is linear, MR curve must have same intercept and twice the slope. So MR curve should have intercept at $14 on price axis, and slope = -2/1 thousand.
- 3 thousand, where MR=MC.
- $11, on demand curve.
- $18 thousand = Rev - TC = price × quantity - AC × quantity.
- $4.5 thousand.
- $1.5 thousand.
- 4 thousand, because anyone willing to pay at least the marginal cost will be served.
- $48 thousand, because with every customer paying a different price, revenue = area of the trapezoid under demand curve down to horizontal axis.
- $24 thousand = Rev - TC = Rev - AC × quantity.
- $0, because consumer surplus is defined as willingness-to-pay minus price, but with perfect price discrimination willingness-to-pay equals price for every customer.
- $0, because with perfect price discrimination, everyone willing to pay the marginal cost is served.
(4) [Competition versus collusion: 16 pts]
- 10 billion.
- $6 (= marginal cost).
- $6.
- Since demand curve is linear, MR curve must have same intercept and twice the slope. So MR curve should have intercept at $16 on price axis, and slope = -2/1 billion.
- 6 billion, where MR = MC.
- $4 (= marginal cost).
- $10, on demand curve.
- $12 billion.
(5) [Monopolistic competition: 12 pts]
- Al's demand equation is
P_{A} = P_{B} + 1 - (Q_{A}/1000)
= 2.50 + 1 - (Q_{A}/1000) = 3.50 - (Q_{A}/1000).
Al's marginal revenue curve must have same intercept and twice slope:
MR = 3.50 - 2(Q_{A}/1000).
- Set MR = MC = $2 and solve to get 750 gallons.
- Insert 750 gallons into demand equation to get $2.75.
- Now Al's demand equation is
P_{A} = P_{B} + 1 - (Q_{A}/1000)
= 4.00 + 1 - (Q_{A}/1000) = 5 - (Q_{A}/1000).
Al's marginal revenue curve must have same intercept and twice slope:
MR = 5 - 2(Q_{A}/1000).
- Set MR = MC = $2 and solve to get 1500 gallons.
- Insert 1500 gallons into demand equation to get $3.50.
- Two points extra credit: same as Version A.
(6) [Monopoly price discrimation: 8 pts]
- 28 percent.
- 6 percent.
- $14.
- $36.
III. Critical thinking
Same as Version A.
Version C
I. Multiple choice
(1)e. (2)c. (3)d. (4)c. (5)c. (6)b. (7)d.
II. Problems
(1) [Economy-wide efficiency: 12 pts]
- $11 (= marginal cost).
- $3 (= marginal cost).
- Firm B (because it has lower marginal cost).
- 5 million, so that marginal costs are equal.
- 9 million, so that marginal costs are equal.
- $6, because each firm will then maximize its own profit by choosing its output level so that its marginal cost equals this price.
(2) [Economy-wide efficiency: 20 pts]
- 2/3 garments.
- 1.5 pounds of food.
- $2, because in competitive equilibrium, price equals marginal cost.
- $3, because in competitive equilibrium, prices reflect the slope of the production possibility curve for the economy as a whole: if the opportunity cost of a unit of clothing is 1.5 units of food, then a unit of clothing must be 1.5 times as expensive as a unit of food.
- $3, because in competitive equilibrium, price equals marginal cost.
- Ashley's budget line should have intercept at 30 on food axis and intercept of 20 on clothing axis.
- -1.5.
- 1.5 pounds of food.
- 2/3 garments.
- 1.5, because Ashley's preferred bundle is at a tangency between her budget line and the highest indifference curve she can reach, and at a tangency the slope of the indifference curve must equal the slope of the budget line.
(3) [Monopoly, price discrimination: 22 pts]
- Since demand curve is linear, MR curve must have same intercept and twice the slope. So MR curve should have intercept at $12 on price axis, and slope = -1/1 thousand.
- 12 thousand, where MR=MC.
- $9, on demand curve.
- $72 thousand = Rev - TC = price × quantity - AC × quantity.
- $18 thousand.
- $6 thousand.
- 16 thousand, because anyone willing to pay at least the marginal cost will be served.
- $160 thousand, because with every customer paying a different price, revenue = area of the trapezoid under demand curve down to horizontal axis.
- $96 thousand = Rev - TC = Rev - AC × quantity.
- $0, because consumer surplus is defined as willingness-to-pay minus price, but with perfect price discrimination willingness-to-pay equals price for every customer.
- $0, because with perfect price discrimination, everyone willing to pay the marginal cost is served.
(4) [Competition versus collusion: 16 pts]
- 20 billion.
- $5 (= marginal cost).
- $5.
- Since demand curve is linear, MR curve must have same intercept and twice the slope. So MR curve should have intercept at $15 on price axis, and slope = -1/1 billion.
- 12 billion, where MR = MC.
- $3 (= marginal cost).
- $9, on demand curve.
- $24 billion.
(5) [Monopolistic competition: 12 pts]
- Al's demand equation is
P_{A} = P_{B} + 1 - (Q_{A}/1000)
= 3.00 + 1 - (Q_{A}/1000) = 4 - (Q_{A}/1000).
Al's marginal revenue curve must have same intercept and twice slope:
MR = 4 - 2(Q_{A}/1000).
- Set MR = MC = $2 and solve to get 1000 gallons.
- Insert 1000 gallons into demand equation to get $3.00.
- Now Al's demand equation is
P_{A} = P_{B} + 1 - (Q_{A}/1000)
= 4.50 + 1 - (Q_{A}/1000) = 5.50 - (Q_{A}/1000).
Al's marginal revenue curve must have same intercept and twice slope:
MR = 5.50 - 2(Q_{A}/1000).
- Set MR = MC = $2 and solve to get 1750 gallons.
- Insert 1750 gallons into demand equation to get $3.75.
- Two points extra credit: same as Version A.
(6) [Monopoly price discrimation: 8 pts]
- 24 percent.
- 8 percent.
- $12.
- $20.
III. Critical thinking
Same as Version A.
[end of answer key]