Suppose a monopolist faces a demand curve Q = aP^-b and that the monopolist has a constant marginal cost of C. The monopolist's profit-maximizing price is

Question

Quizplus · Accepted Answer

To find the profit-maximizing price, we need to take the derivative of the monopolist's profit with respect to price and set it equal to zero:

π = P(Q)Q - C(Q)

where Q = aPS1U1P1-bS1S1P0

π = (aPS1U1P1-bS1S1P0 - C)Q

π = (aPS1U1P1-bS1S1P0 - C)(aPS1U1P1-bS1S1P0)

π = a^2 P^2 S1U1P1^2 - aPSCS1U1P1P0 - aCP0S1S1P0 + bCS1S1P0P

dπ/dP = 2a^2 PS1U1P1^2 - aCS1U1P0 + bCS1S1P0 = 0

P = [ aCS1U1P0 - bCS1S1P0 ] / [ 2a^2 S1U1P1^2 ]

P = C [ aP0 / b - S1S1P0 ] / [ 2a^2 S1U1P1^2 ]

P = C / [ 2aU1P1^2/b - 1 ]

P = C [ 1 / ( 1 - 1/b ) ] / [ 2aU1P1^2 / ( b ( b - 1 ) ) ]

P = C [ 1 / ( 1 - 1/b ) ]

Suppose a Monopolist Faces a Demand Curve Q = AP-B P=C(1−1/b)P = C ( 1 - 1 / b )P=C(1−1/b)

Suppose a Monopolist Faces a Demand Curve Q = AP^-B $P = C ( 1 - 1 / b )$