Since the equilibrium in the previous problem has positive profit per firm, it i
ID: 1119153 • Letter: S
Question
Since the equilibrium in the previous problem has positive profit per firm, it is not a long-run equilibrium. However, since the AC curve in the problem is upward-sloping everywhere, it is not possible to construct a zero-profit equilibrium given the assumptions of the problem (this outcome requires a U-shaped AC curve. This problem will consider an alternative example where a long-run equilibrium exists. Let the total cost function for an individual firm be given by C 204Q-40a2+ 2Q3. Compute average cost for Q1, 2, 3..,14, 15. a) Using your results, find the long-run equilibrium price in the market. This price is given by p = (don't include a $ sign in your answer), and output per firm is Q = b) Suppose that the (inverted) market demand curve for the product is given by Q 50000 10000P. What total quantity is demanded at the long-run equilibrium price? c) From (b), you know how much total output must be delivered by all firms operating in the long-run equilibrium. Using this number along with the results from part (a), compute the number of firms in the industry in the long-run equilibrium. This number isExplanation / Answer
C = 204Q - 40Q2 + 2Q3
Average cost (AC) = C / Q = 204 - 40Q + 2Q2
(a) In long run equilibrium, p = MC = AC
MC = dC / dQ = 204 - 80Q + 6Q2
Equating with AC,
204 - 80Q + 6Q2 = 204 - 40Q + 2Q2
4Q2 = 40Q
4Q = 40 (Dividing by Q, assuming Q is non-zero)
Q = 10 [Firm output]
P = AC = 204 - (40 x 10) + (2 x 10 x 10) = 204 - 400 + 200 = 4
(b)
When P = 4,
Q = 50000 - (10000 x 4) = 50000 - 40000 = 10000 [Market output]
(c)
Number of firms = Market output / Firm output = 10000 / 10 = 1000