Question

A monopolistic market structure is facing the following demand curve, Q=1800-25P. It's STC total cost is given by 100+7Q+0.025Q square. Find the following.

A. His profit maximizing quantity, price and TR.

B. If the firm wants to incur an average selling cost of Rs. 33 per unit., will the firm face below, above or just normal profits.. support ans with calculation

Answer 1

Given, demand function: Q=1800-25P

Hence inverse demand function can be written as -

25P=1800-Q

Or, P = 72 - (Q/25).

Now Total Revenue: Price ×Quantity.

Or, TR=P×Q

Or,TR=[72-(Q/25)]×Q

Or, TR=72Q - [(Q^2)/25]

Hence profit maximizing quantity is: Q*=500

From inverse demand function we can calculate the Profit maximizing price-

P=72-(500/25)

Or,P=72-20

Or, P=52

Hence profit maximizing price:P*=52.

Profit Maximizing Total Revenue=P*×Q*

Or, Total Revenue= 500×52 = 26,000.

B) At profit maximizing level the firm is selling Q*=500 units of output.

If Average Cost is = 33.

Then total cost of production= (500×33) = 16,500.

It seems at Q*=500, Total Revenue is higher than Total Cost of production. Hence the firm is earning profit by producing the output of amountQ*=500.

The firm earns an profit of amount given by -

Profit = Total Revenue - Total Cost

Or, Profit= 26000 - 16500

Or, Profit = 9500.

Hence the firm is earning a positive profit at average cost of 33.