Answer to Question #261111 in Microeconomics for Shujaa

Question

A company estimates that the demand for its product fluctuates with the

price it charges. The demand function is (05 Marks)

q= 280,000 – 400p

Where q equal the number of units demanded and p equals the price in dollars.

The cost of producing q units of the product is estimated by the function

C = 350,000 + 300q + 0.0015q2

i. Determine the number of units that should be produce in order to

maximize the annual profit.

ii. What price should be charged?

iii. What is the annual profit expected to equal?

Answer 1

Demand Function, Q = 280,000-400P

Inverse Demand Function, P = (280,000-Q)/400 = 700 - Q/400

Total Revenue = Price x Quantity = (700-Q/400)xQ = 700Q - Q²/400

Marginal revenue function =

Total Cost function = 350,000+300Q+0.0015Q²

Marginal Cost =

Profit is maximized when Marginal Cost = Marginal Revenue (Price)

300+0.003Q = 700-0.005Q

0.003Q+0.005Q = 700-300

0.008Q=400

Q=400/0.008 = 50,000

i) The firm should produce 50,000 units to maximize its profit

ii) Price that should be charged = Marginal Revenue at 50,000 units of output = $(700 -0.005(50,000)) = $(700 - 250) = $ 450

iii)At maximum profit condition, Q = 50,000

Total Revenue = 700Q-0.005Q² = 700 x 50,000 - 0.005 x 50,000² = $22,500,000

Total Cost = 350,000+300Q+0.0015Q² = 350,000+300 x 50,000 + 0.0015 x 50,000² =$19,100,000

Annual Profit = Total Revenue - Total Cost = $22,500,000-$19,100,000 = $3,400,000

Therefore, expected annual profit = $3,400,000