Problem Set 2
Producer Theory
Cost minimization, profit maximization, and competitive equilibrium using calculus. Work through the optimality conditions before selecting your answer.
Key Conditions
Cost minimization:
MRTS = MPL/MPK = w/r
MRTS = MPL/MPK = w/r
Cobb–Douglas Q = KαLβ:
MPL = βQ/L MPK = αQ/K
MPL = βQ/L MPK = αQ/K
Profit max (any firm):
MR = MC (P = MC if competitive)
MR = MC (P = MC if competitive)
Monopoly MR:
MR = P + Q(dP/dQ)
MR = P + Q(dP/dQ)
Min ATC:
d(ATC)/dQ = 0 ⇒ MC = ATC
d(ATC)/dQ = 0 ⇒ MC = ATC
Break-even price:
P* = min ATC
P* = min ATC