Question

Given a perfectly competitive firm in the output market where: P0= exogenous price, C(Q) = cost function where: C’ > 0, C” > 0. a)State the firm’s profit function in terms of Q. b)Find the F.O.C. that maximizes profits at Q*. c)Interpret the F.O.C. d)Find the S.O.C. that maximizes profits at Q*. e)Interpret the S.O.C. f)Find dQ*/dP0using the implicit function rule on the F.O.C. g)Interpret the derivative in (f) economically.

Answer 1

a) Profit function = Profit = P0Q - C(Q)

b) F.O.C is:

d(Profit)/dQ =0

P0* = C', where C'>0

c) The first order condition states that equilibrium price = marginal cost is the condition for profit maximization under perfect competition

d) S.O.C is:

d(dProfit/dQ)dQ < 0

C'' > 0

e) Second order condition states that at point of equilibrium for profit maximzation, the rate of change of slope of total cost TC curve should be greater than zero

f) As dP0/dQ* = 0 for Perfect competition, this implies dQ*/dP0 = infinite, for Perfect competition

g) If the price change by minimal value, the quantity demanded would change by infinite value