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Suppose that the inverse demand equation for a firm's product is P = 420?10Q. (11.2) The...

Suppose that the inverse demand equation for a firm's product is P = 420?10Q. (11.2) The total cost is given by the equation TC = 500+20Q^2. (11.3) a. What are the profit-maximizing price and quantity from a single-price strategy? b. Given your answer to part a, what is the firm's total operating profit? What is the firms total operating profit if it engages in perfect first-degree price discrimination? What is the firm's total economic profit?

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Expert Solution

Suppose that the inverse demand equation for a firm's product is P = 420?10Q. The total cost is given by the equation TC = 500+20Q^2.

a. What are the profit-maximizing price and quantity from a single-price strategy?

Total revenue function is TR = PQ = (420 - 10Q)Q = 420Q - 10Q^2

Marginal revenue MR = dTR/dQ = 420 - 20Q

MC = dTC/dQ = 40Q

Profit maximizing quantity determined at

420 - 20Q = 40Q

420 = 60Q

Q = 7 units

Profit maximizing price is P = 420 - 10*7 = $350 per unit. This is shown by point A

b. Given your answer to part a, what is the firm's total operating profit?

Operating profit = yellow shaded region = (350 - 280)*7 + 0.5*(280 - 0)*7 = 1470

Total net profit = 1470 - 500 = 970

What is the firms total operating profit if it engages in perfect first-degree price discrimination?

For first degree price discrimination, P = MC rule is used

420 - 10Q = 40Q

Q = 8.4 units and price = P = 420 - 10*8.4 = $336. This is shown by point B

New Profit is entire consumer surplus = 0.5*(420 - 336)*8.4 = 352.8. Total operating profit = 352.8 + 0.5*(336 - 0)*8.4 = 1764

What is the firm's total economic profit?

Total economic profit = 1764 - 500 = 1264

Rahul Sunny answered 2 years ago
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