Question

The cost function of a monopoly firm is TC = 10 + 2Q where TCq is the total cost of producing the quantity. The demand in this market is expressed by the equation Q 14 = 14 – P where P denotes the price. Estimate the profit to be made by the monopolist.

Answer 1

$Profit= TR-TC$

$TC=10+2Q$

From the demand curve:

$Q=1-0.71P$ f

$TR=(1-0.071P)\times{P}=P-0.071P^{2}$

$Profits=(P-0.071P^{2})-(10-2Q)$

$=(p-0.071P^{2})-(10+2-0.142P)$

$=-0.071P^{2}+1.143P-12$

Using the quadratic formula to solve for P:

$P=\frac{-b+-√(b^{2}-4ac)}{2a}$

$P=\frac{-1.143+-√(1.143^{2}-4×-0.071×12)}{2×-0.071}$

$P=6.91$

$Q=1-0.071×6.91=0.51$

Therefore

$TR=6.91×0.51=3.52$

$TC=10+2×0.51=11.02$

$Profit=3.52-11.02=-7.5$

Therefore the firm is making a loss.