Question

Assume that Lakamuun joint is a monopolist that produces plates of TZ at Accra 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

(i) The output for which profits are maximized (or losses minimized) is:

MR = MC.

(ii) MR = TR'(q) = 96 - 8q,

MC = C'(q) = (AC×q)' = 6 + q,

96 - 8q = 6 + q,

9q = 90,

q = 10 units,

p = 96 - 4×10 = 56.

(iii) Total profits at this price-output combination are:

$TP = TR - C = 56×10 - (100 + 6×10 + 0.5×10^2) = 350.$

(iv) the firm should continue product in the short run, because it receives positive economic profits.