Assume a monopolist firm has the cost function C = 10800 +-Q2 And faces the dema

Question

Assume a monopolist firm has the cost function C = 10800 +-Q2 And faces the demand function p = 5000-3Q Find the equation for marginal cost Find the equation for marginal revenue Derive the monopolist's price and quantity assuming they can only charge one price to all consumers Find the monopolist's profits Describe how the monopolist should set prices if they are suddenly able to measure each individual's maximum willingness to pay, and can prevent people from reselling the good. a. b. c. d. e.

Explanation / Answer

Answer
a)
MC is the first derivative of total cost
MC=dC/dQ=0.5Q

b)
TR=P*Q=5000Q-(4/3)Q^2
MR=dTR/dQ=5000-(8/3)Q
c)
the monopoly produces at MR=MC to maximize profit because themarginal profit is zero at this place (Marginap profit=marginal revenue-marginal cost)
0.5Q=5000-(8/3)Q
0.5Q+(8/3)Q=5000
9.5Q=15000
Q=15000/9.5=1578.94737
P=5000-(4/3)*1578.94737=2894.73684

d)
Profit=TR-TC
TR=P*Q=2894.73684*1578.94737=4570637.12
TC=10800+0.25*(1578.94737^2)=634068.699
Profit=4570637.12-634068.699=3936568.42
The profit is $3936568.42

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