Consider a monopolist whose total cost function is TC = 20 + 5Q + 0.5Q2 and whos

Question

Consider a monopolist whose total cost function is TC = 20 + 5Q + 0.5Q2 and whose marginal cost function is MC = 5 + Q. The demand function for the firm's good is P = 80 - 0.25Q. The firm optimizes by producing the level of output that maximizes profit or minimizes loss. If the firm uses a uniform pricing strategy, then the firm will:

a.) produce 50 units of output, charge a price of $68, and earn a profit of $1880
b.) produce 50 units of output, charge a price of $68, and earn a profit of $2712
c.) produce 60 units of output, charge a price of $65, and earn a profit of $2443
d.) produce 60 units of output, charge a price of $65, and earn a profit of $3240
e.) shut down and suffer a loss of $1274

Explanation / Answer

Answer
The firm produces at MR=MC
MR=80-0.5Q........the MR is double sloped than the demand curve
equating MR=MC
80-0.5Q=5+Q
1.5Q=75
Q=50
P=80-0.25*50
=67.5
rounding
P=68
Profit=TR-TC
TR=P*Q=50*68=3400
TC=20+5*50+0.5*50^2=1520
Profit=3400-1520=1880
option a

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