Question

Assume that Lakamuun joint is a monopolist that produces plates of TZ at konongo has the following average cost functions, AC= 100/q + 6 + 0.5q. If the demand function is given by: q= 24 - 1/4p.


(i)Set up the profit maximizing problem of the firm


ii. Compute the output-price combination that maximizes the profit of the firm


iii. What is the maximum profit


iv. Explain extensively if the firm should or should not continue product in the short run.

Answer 1

Monopoly earns the highest profit when its MR is equal to MC. To find MR we need TR which is P*Q.

From demand equation, $P = 96- 4*Q$

So, $TR = 96*Q - 4*Q^2$. Thus, $MR = 96 - 8*Q$.

To caclulate MC we need TC. $TC = AC*Q=100+6*Q+0.5*Q^2$

$MC = 6+Q$.

As $MC=MR$,

$6+Q = 96 - 8*Q$ (i)

Q = 10, P = 56 (ii).

The maximum profit(TP) is the difference between total revenue and total cost.

So, $TR = 560. TC = 100+60+50 = 210.$

So, $TP = 560 - 210 = 350$(ii).

(iii) As the firm's average variable cost is $AVC = 100/Q +0.5*Q = 10+5 = 15$ is less than the equilibrium price(P = 56), the firm should continue to operate in short-run.