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. (6Marks)

Answer 1

$P = 1200-2Q$

$C= Q^3-61.25Q^2+ 1528.5Q + 2000$

Equilibrium output occurs when $MR= MC$

Total Revenue$= P× Q$

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

Marginal Revenue MR is the first derivative of Total Revenue TR

$\frac{dTR}{DQ}$ $= 1200- 4Q$

Marginal Cost, MC is

$\frac{DC}{DQ} = 3Q^2- 122.5Q+1528.5$

At equilibrium

MR= MC

1200- 4Q = $3Q^2 - 122.5Q +1528.5$

$Q = 36.5$

Monopolist Price is;

$P =1200-2(36.5)= 1127$

Profit = TR- TC

TR=$1200(36.5)-2(36.5^2)= 40535.5$

TC = $24817.06$ ( using Cost function with Q= 36.5)

Profit =$40535- 24817.06= 15717.94$