QUIZ 2 ANSWER KEY
Competitive Firms
Version A
I. Multiple choice [3 pt each: 24 pts total]
(1)b. (2)a. (3)b. (4)f. (5)a. (6)b. (7)a. (8)d.
II. Problems
(1) [Profit maximization: 20 pts]
- MR(Q) = 15 - (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(Q) = 3 + (Q/20).
- Set MR=MC and solve to get Q*=80.
(2) [Profit maximization while taking price as given: 10 pts]
- Find MC(Q) as dTC/dQ. Set MC(Q)=P=9 and solve to get Q*=400.
- Profit = Revenue - TC(Q). Since price is taken as given at $9, revenue = $9 × 400 = $3600. TC(400) = $2800. So profit = $800.
(3) [Short-run cost curves and supply: 20 pts]
- $1 = MC(700).
- $12 thousand = SATC x 1500.
- $8 = minimum SATC.
- $2 = minimum SAVC.
- 1600 flashlights (using rule P=MC).
- profit because price > breakeven price.
- 1400 flashlights because price < breakeven price.
- loss because price < breakeven price.
- zero flashlights because price < shutdown price.
- loss equal to SFC.
(4) [Long-run cost and supply: 20 pts]
- MC(q) = dTC/dq = 3 q^{2} - 200 q + 2520.
- AC(q) = TC/q = q^{2} - 100 q + 2520.
- Breakeven price = minimum AC. So set derivative of AC equal to zero and solve to get q_{ES}=50. Then substitute AC(50) = $20 = breakeven price.
- Given the assumptions, long-run industry supply is a horizontal line at minimum AC = $20.
III. Critical thinking [6 pts]
We are asked to find SFC, which equals SAFC × Q. Now SAFC = SATC - SAVC. At Q=1000, for example, SATC = $10 and SAVC = $2, so SAFC = 10 - 2 = $8. Therefore, SFC = $8 × 1000 = $8000. (Calculations at different values of Q should result in an identical final answer for SFC.)
Version B
I. Multiple choice [3 pt each: 24 pts total]
(1)a. (2)d. (3)c. (4)f. (5)b. (6)c. (7)c. (8)a.
II. Problems
(1) [Profit maximization: 20 pts]
- MR(Q) = 17 - (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(Q) = 2 + (Q/20).
- Set MR=MC and solve to get Q*=100.
(2) [Profit maximization while taking price as given: 10 pts]
- Find MC(Q) as dTC/dQ. Set MC(Q)=P=13 and solve to get Q*=800.
- Profit = Revenue - TC(Q). Since price is taken as given at $13, revenue = $13 × 800 = $10400. TC(800) =$7200. So profit = $3200.
(3) [Short-run cost curves and supply: 20 pts]
- $13 = MC(700).
- $10 thousand = SATC x 900.
- $7 = minimum SATC.
- $4 = minimum SAVC.
- 1600 flashlights (using rule P=MC).
- loss because price < breakeven price.
- zero flashlights because price < shutdown price.
- loss equal to SFC.
- 1900 flashlights.
- profit because price > breakeven price.
(4) [Long-run cost and supply: 20 pts]
- MC(q) = dTC/dq = 3 q^{2} - 160 q + 1630.
- AC(q) = TC/q = q^{2} - 80 q + 1630.
- Breakeven price = minimum AC. So set derivative of AC equal to zero and solve to get q_{ES}=40. Then substitute AC(50) = $30 = breakeven price.
- Given the assumptions, long-run industry supply is a horizontal line at minimum AC = $30.
III. Critical thinking [6 pts]
We are asked to find SFC, which equals SAFC × Q. Now SAFC = SATC - SAVC. At Q=1000, for example, SATC = $10 and SAVC = $5, so SAFC = 10 - 5 = $5. Therefore, SFC = $5 × 1000 = $5000. (Calculations at different values of Q should result in an identical final answer for SFC.)
[end of answer key]