Question

1. If the inverse demand curve of profit maximizing monopolist is given as P =1200 − 2Q , and cost function as

 C = Q3 − 61.25Q²+1528.5Q + 2000, find equilibrium output level, monopolist price, and profit.

Answer 1

Solution

Max profit $=R(Q)- C(Q)$

$R(Q) = 1200Q-2Q^2$

$1200Q-2Q^2-(Q^3-61.25Q^2$ $+1528.5Q+2000$ )

=$- Q3+59.25Q2- 328.5Q-2000$

Max Profit =$- Q3+59.25Q2-328.5Q-2000$

Max Profit= π

$π'(Q)=-3Q2+118.5Q-328.5$

$π'(Q)=-6Q+118.5$

$π'(Q)=-3Q2+118.5Q-328.5=0$

Using the quadratic formula

Q=3

Q=6

$π"(3)=100.5> 0$ is the relative minimum

$π"(36.5)=-100.5< 0$ relative maximum

For maximum profits the firm should produce 36.5 units of output.

Q=36.5, π=16318.44