ANSWER KEY: COMPETITIVE FIRMS
Quiz 2 Version A
(1)d. (2)c. (3)a. (4)b. (5)a. (6)b. (7)b. (8)d. (9)b. (10)b.
Quiz 2 Version B
(1)b. (2)c. (3)b. (4)a. (5)c. (6)a. (7)d. (8)c. (9)c. (10)c.
Test 2 Version A
(1) [Profit maximization: 20 pts]
- MR = dRev/dq = 20 - (q/5).
- 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 + (q/10).
- Set MR=MC and solve to get q*=60.
(2) [Profit maximization while taking price as given: 20 pts]
- Set MC(q) = P and solve to find q*. Here, MC(q) = 2 + (q/50) and P is given as $7, so q* = 250.
- Profit = Revenue - TC(q*) = P × q* - [2q* + (q*^{2}/100)]
= $625.
(3) [Short-run cost curves and supply: 20 pts]
- $4 = MC(600), since marginal cost is defined as the change in total cost caused by a one-unit change in output.
- $12 thousand = SATC × 1200, since SATC is defined as STC divided by output.
- $9 = minimum SATC.
- $5 = minimum SAVC.
- 1600 shovels (using rule P=MC).
- loss because price < breakeven price.
- 1800 shovels because price > breakeven price.
- profit 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} - 160 q + 1605.
- AC(q) = TC/q = q^{2} - 80 q + 1605.
- Breakeven price = minimum AC. So set derivative of AC equal to zero and solve to get q_{ES}=40.
- AC(q_{ES}) = $5 = breakeven price.
- Given the assumptions, long-run industry supply is a horizontal line at minimum AC = $5.
Critical thinking [10 pts]
- The firm should not necessarily choose a level of output where average cost is lowest. The competitive firm's profit-maximizing level of output depends on the market price, which the firm takes as given. If the market price is greater than the firm's minimum average cost, the firm should choose an output level such that price = marginal cost. If the market price is less than the firm's minimum average cost, the firm choose an output level of zero—that is, it should shut down. (Full credit credit requires a graph of marginal and average cost, showing how output is determined by P=MC.)
Test 2 Version B
(1) [Profit maximization: 20 pts]
- MR = dRev/dq = 25 - (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 + (q/20).
- Set MR=MC and solve to get q*=160.
(2) [Profit maximization while taking price as given: 20 pts]
- Set MC(q) = P and solve to find q*. Here, MC(q) = 3 + (q/40) and P is given as $8, so q* = 200.
- Profit = Revenue - TC(q*) = P × q* - [3q* + (q*^{2}/80)]
= $500.
(3) [Short-run cost curves and supply: 20 pts]
- $12 = MC(1900), since marginal cost cost is defined as the change in total cost caused by a one-unit change in output.
- $25 thousand = SATC × 2500, since SATC is defined as STC divided by output.
- $2 = minimum SAVC.
- $7 = minimum SATC.
- 1300 shovels (using rule P=MC).
- loss because price < breakeven price.
- zero flashlights because price < shutdown price.
- loss equal to SFC.
- 1800 shovels because price > breakeven price.
- profit because price > breakeven price.
(4) [Long-run cost and supply: 20 pts]
- MC(q) = dTC/dq = 1.5 q^{2} - 120 q + 1806.
- AC(q) = TC/q = 0.5 q^{2} - 60 q + 1806.
- Breakeven price = minimum AC. So set derivative of AC equal to zero and solve to get q_{ES}=60.
- AC(q_{ES}) = $6 = breakeven price.
- Given the assumptions, long-run industry supply is a horizontal line at minimum AC = $6.
Critical thinking [10 pts]
[end of answer key]