Question

If there is one firm in the industry, and C(Q)=100+2Q² , and demand is as follows: P=90-2Q , then find price, quantity and profit.

Answer 1

If there is one firm in the industry, then its a monopoly. A profit maximizing monoply produces at the point where MR=MC and sets it's profit maximizing price at the point where profit maximizing quantity lies on the demand curve.

The demand curve is given as, P = 90 - 2Q

Multiplying both sides by Q we get, PQ = 90Q - 2Q² = TR

Or, MR = d(TR)/dQ = 90 - 4Q

And, the cost function is given as, C = 100 + 2Q²

Or, MC = d(C) /dQ = 0 + 4Q = 4Q

Setting MR = MC, we get, 90 - 4Q = 4Q

Or, 8Q = 90

Or, Q = (90/8) = 11.25

Now from the demand equation we get, P = 90 - (2*11.25) = 67.5

Therefore, profit maximizing price is $67.5 and profit maximizing quantity is 11.25 units.

At this quantity, Total cost = 100 + 2(11.25)² = $353.125

Total revenue = price * quantity = $(67.5 * 11.25) = $759.375

Therefore, profit = total revenue - total cost = $(759.375 - 353.125) = $406.25

answered by: anonymous