(30 pts) A competitive firm has a cost function that satisfies the following: (i
ID: 1142511 • Letter: #
Question
(30 pts) A competitive firm has a cost function that satisfies the following: (i) PS (y)- 11 (y) 4 for all y, (ii) MC(0) AVC(0) = 2 and (iii) AVC(y)-y + 2 (a) Derive the firm's total cost function C (y), marginal cost function MC (), average variable cost function AVC(v), and average cost function AC (u). (5 pts) (b) Show MC, AVC, and AC functions on a graph. (5 pts) (c) Derive the short-run supply curve for this firm. (5 pts) (d) If the market price is p 12. How many units will the firm produce? (5 pts) (e) Determine the associated profit and producer surplus for the firm. (5 pts) (f) How do the maximum profit related to the producer's surplus? (5 pts)Explanation / Answer
a profit maximising condition is MC=MR
Revenue=P*Q=(200-3Q)*Q
hence MR= 200-6Q
MC=20=200-6Q
therefore we get Q=30 ;
b) the price=200-3*30=$ 110
c) profit=P*Q-20*Q
110*30-20*30=$ 2700
d) consumer surplus= 1/2*90*30=1350
e) deadweight loss= 1/2*30*90=1350
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