Question

1) Assume that a firm faces the following cost function: TC(q) = 980 + 10q2 – 5q + 20 a) Derive the long-term supply curve for this individual firm. b) If market price is equal to p=40 what quantity would be supplied? c) Calculate profit at p=300. d) with free entry and exit and identical firms what would be the long term supply curve for this industry?

Answer 1

Total cost, TC = 980 + 1092 – 5q + 20

Part (A)

firm's long-run supply function is the increasing part of its long run marginal cost curve above the minimum of its long run average cost

BTC Marginal cost, MC => -= 209 - 5

TC 980 100 59 20 1000 Average cost, AC = - = - +- - 3 + = = = --5+ 109 99 9 9 9 Differentiating with respect to q to minimize Average cost 2.AC -1000 - +10 =0 aqq? – 1000 = -1092 q* = -1000,- 10 = 100 9 +

Since output produced by a firm cannot be negative

Therefore, average cost is at its minimum when output produced is 10 units

AC 2000 aq? at g= 10 22 AC 2000 2000 2q2 3 = 1000 = 2 :. Average cost is minimized at q = 10

i Long run supply curve for the firm is P= 2q - 5 with q> 10 or P +5 q=-20 with q> 10

Part (B)

If price, P = 40 then quantity supplied is P +5 40+5 45 9= 20 = 20 = 50 = 2.25

Part (C)

If Price, P = 300 Profits of firm, 7 = Total Revenue, TR - Total Cost, TC T = P*9-980 – 100° +59 - 20 = 300g – 1000 – 1092 +59 1 = 3059 – 1000 – 1002 Differentiating with respect to q and equating to 0 to maximize profits OT = 305 - 20q = 0 305 = 204 305 да 9= 20 = 15.25 227 a = -20 < 0 :: profits marimized at q = 15.25

Part (D)

With free entry and exit and identical firms, the industry supply curve will be n times firm supply assuming there are are 'n' firms in the industry at the moment.

Long-term industry supply curve P +5 n(P + 5) Q = nq = n + (- 20