In a competitive industry consistin g of 10,000 firms, the short-run marginal co
ID: 1203005 • Letter: I
Question
In a competitive industry consistin g of 10,000 firms, the short-run marginal cost curve for each firm is given by MC - 200 + 30Q. The demand curve faced by the industry is given as p - 400 -0.002Q. a. Find the equilibrium price and quantities for the industry and each firm Answer. b. Find the producer and consumer surpluses at the equilibrium price. Note that CS and PS formulae - 1/2(Base) x Height Answer. 3. If each competitive firm in an industry has the short-run cost function C - 50 + 5q + q^2, and the market price (P) is $35, what is the profit-maximizing output level for each firm? What is its total revenue? What is its profit? At what price does it shut down?Explanation / Answer
Equilibrium for Industry will be where
P = MC 0r Quantity demanded = Quantity supplied
S0, P = 40,00,000 - 20Q = 20,00,000 + 3,00,000Q
300020Q = 20,00,000
Q* = 6.66
P* = 400 - 0.002Q =400 - 0.002*6.66 = 399.99
consumer surplus = 1/2(400 - 399.99)*6.66
= 44
Producer Surplus = 1/2(399.99-200)*6.66
= 13310000
3.
Profit is maximized at P= MC
MC = dTC/dQ = 5 + 2Q
S0, 35 = 5 + 2Q
Q* = 15
P* = 35
TR = P*Q = 35*15 = 525
Profit = TR - TC
TC = 50 + 5Q + Q^2 = 50 + 5*15 + (15)^2 = 350
So Profit = 525 - 350 = 175
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