(1)a. (2)c. (3)b. (4)c. (5)b. (6)b. (7)b. (8)b. (9)c. (10)d.
(11)b. (12)c. (13)c. (14)d. (15)b.
6 percent.
(2) [Profit maximization: 10 pts]
- MR = dTR/dq = 10 - (q/10).
- Firm does not take price as given because marginal revenue is not constant--it depends on the firm's own output level q.
- MC = dTC/dq = 1 + (2q/10).
- Set MR=MC and solve to get q*=30.
(3) [Short-run cost curves and supply: 20 pts]
- $180 thousand = SATC × 15 thousand, because SATC is defined as STC divided by output.
- $150 thousand = SAVC × 15 thousand, because SAVC is defined as SVC divided by output.
- $30 thousand, because STC = SVC + SFC.
- $6 = MC(4 thousand), since marginal cost is defined as the change in total cost caused by a one-unit change in output.
- $10 = minimum SATC.
- $7 = minimum SAVC.
- 9 thousand (using rule P=MC).
- loss because price < breakeven price.
- 12 thousand (using rule P=MC).
- profit because price > breakeven price.
(4) [Long-run cost and supply: 20 pts]
- MC(q) = dTC/dq = 0.15 q^{2} - 4 q + 23.
- AC(q) = TC/q = 0.05 q^{2} - 2 q + 23.
- Efficient scale is value of q that minimizes AC(q). So set derivative of AC equal to zero and solve to get q_{ES}=20.
- Breakeven price = minimum AC = AC(q_{ES}) = $3.
- Given the assumptions, long-run industry supply is a horizontal line at minimum AC = $3.
(5) [Consumer surplus, producer surplus: 12 pts]
- $10 = height of demand curve.
- $6 = height of demand curve - price.
- $2 = height of supply curve.
- $2 = price - height of supply curve.
- $72 million = area of triangle bounded by demand curve, vertical axis, and price.
- $18 million = area of triangle bounded by supply curve, vertical axis, and price.
(6) [Welfare analysis of price controls: 18 pts]
- $5.
- 6 million pounds.
- excess demand.
- 6 million pounds.
- decrease.
- $16 million.
- increase.
- $4 million.
- $12 million.
III. Critical thinking [5 pts]
- ABC Company will perceive the demand for its own output to be more elastic than demand for the market as a whole because it has only small market share. If other furniture makers keep their output levels constant, a large percent change in ABC's output amounts to a small percent change in market output. Since elasticity equals percent change in quantity divided by percent change in price, this implies that ABC's elasticity will be larger in absolute value than the elasticity for the market as a whole. In particular, if other furniture makers keep their output levels constant, ABC's perceived elasticity of demand is ε/S = -1.5/0.05 = -30.
- Since supply is perfectly elastic (horizontal), deadweight loss from the government restrction is the area of a triangle:
(1/2) ΔQ × ΔP
= (1/2) (%chg Q) Q × (%chg P) P
= (1/2) (%chg Q) × (%chg P) × PQ
Now (%chg P) is given as 5 percent. The elasticity of demand is given as -2, so (%chg Q) must be 10%. PQ is given as $1 million. So deadweight loss equals $2500. (Full credit requires a graph showing demand, perfectly elastic supply, and the DWL triangle.)
Version B
I. Multiple choice
(1)b. (2)d. (3)a. (4)d. (5)a. (6)c. (7)a. (8)c. (9)d. (10)b.
(11)c. (12)b. (13)d. (14)b. (15)a.
II. Problems
(1) [Using price elasticity of demand: 10 pts]
- elastic.
- decrease.
- 6 percent.
- decrease.
- 1 percent.
(2) [Profit maximization: 10 pts]
- MR = dTR/dq = 14 - (q/20).
- Firm does not take price as given because marginal revenue is not constant--it depends on the firm's own output level q.
- MC = dTC/dq = 2 + (2q/20).
- Set MR=MC and solve to get q*=80.
(3) [Short-run cost curves and supply: 20 pts]
- $160 thousand = SATC × 20 thousand, because SATC is defined as STC divided by output.
- $120 thousand = SAVC × 20 thousand, because SAVC is defined as SVC divided by output.
- $40 thousand, because STC = SVC + SFC.
- $3 = MC(4 thousand), since marginal cost is defined as the change in total cost caused by a one-unit change in output.
- $6 = minimum SATC.
- $3 = minimum SAVC.
- 15 thousand (using rule P=MC).
- profit because price > breakeven price.
- 0 thousand, because price < shutdown price.
- loss, equal to short-run fixed cost, SFC.
(4) [Long-run cost and supply: 20 pts]
- MC(q) = dTC/dq = 0.06 q^{2} - 4 q + 56.
- AC(q) = TC/q = 0.02 q^{2} - 2 q + 56.
- Efficient scale is value of q that minimizes AC(q). So set derivative of AC equal to zero and solve to get q_{ES}=50.
- Breakeven price = minimum AC = AC(q_{ES}) = $6.
- Given the assumptions, long-run industry supply is a horizontal line at minimum AC = $6.
(5) [Consumer surplus, producer surplus: 12 pts]
- $9 = height of demand curve.
- $3 = height of demand curve - price.
- $4 = height of supply curve.
- $2 = price - height of supply curve.
- $40.5 million = area of triangle bounded by demand curve, vertical axis, and price.
- $13.5 million = area of triangle bounded by supply curve, vertical axis, and price.
(6) [Welfare analysis of price controls: 18 pts]
- $5.
- 8 million pounds.
- excess supply.
- 6 million pounds.
- increase.
- $15 million.
- decrease.
- $18 million.
- $3 million.
III. Critical thinking
Same as Version A.
[end of answer key]