Question

ABC Co is estimating next year’s profit. Due to the presidential election and pandemic market demand is uncertain. The estimated inverse demand that shows that 40% of the time P=5,000 – 10Q and the 60% time P= 4,000 – 20Q. The firm’s cost function is C(Q) = 100,000+ 400Q. What is the expected profit maximizing quantity and expected profit?

Answer 1

The estimated inverse demand shows that 40% of the time P = 5,000 - 10Q and the 60% of the time P = 4,000 - 20Q

Derive expected demand function -

P = [0.40 * (5,000 - 10Q)] + [0.60 * (4,000 - 20Q)]

P = [2,000 - 4Q] + [2,400 - 12Q]

P = 4,400 - 16Q

Derive the expected total revenue -

TR = P * Q = [4,400 - 16Q] * Q = 4,400Q - 16Q²

Derive the expected marginal revenue -

MR = dTR/dQ

MR = d(4,400Q - 16Q²)/dQ

MR = 4,400 - 32Q

Total cost function is as follows -

TC = 100,000 + 400Q

Derive the marginal cost function -

MC = dTC/dQ

MC = d(100,000 + 400Q)/dQ

MC = 400

Profit-maximization condition is as follows -

MR = MC

4,400 - 32Q = 400

32Q = 4,000

Q = 4,000/32 = 125

The expected profit-maximizing quantity is 125 units.

Calculate the expected profit -

Expected profit = Total revenue - Total cost

Expected profit = [4,400Q - 16Q²] - [100,000 + 400Q]

Expected profit = [(4,400 * 125) - 16(125)²] - [100,000 + (400 * 125)]

Expected profit = 300,000 - 150,000

Expected profit = 150,000

The expected profit is $150,000.