2. Assume a firm’s inverse demand for its product is P = 150 – Q and total cost
ID: 1127670 • Letter: 2
Question
2. Assume a firm’s inverse demand for its product is P = 150 – Q and total cost is TC = 500 + 50Q for a monopolistically competitive firm: a. Find the firm’s marginal revenue (MR) and marginal cost (MC). b. Calculate the profit-maximizing price and quantity in the short-run. c. Calculate the firm's profit in the short-run. d. Explain what happens in the market in response to short-run profitability. e. Calculate the profit-maximizing price and quantity in the long-run (there is a pair of answers). f. Calculate the firm's profit in the long-run-run (there is a pair of answers). Note: Use sqrt(8,000) = 89. my main concern is part f.
Explanation / Answer
(a)
Total revenue (TR) = P x Q = 150Q - Q2
MR = dTR/dQ = 150 - 2Q
TC = 500 + 50Q
MC = dTC/dQ = 50
(b) Profit is maximized when MR = MC:
150 - 2Q = 50
2Q = 100
Q = 50
P = 150 - 50 = $100
(c)
TR = $100 x 50 = $5000
TC = 500 + (50 x 50) = 500 + 2500 = $3000
Profit = TR - TC = $5000 - $3000 = $2000
(d)
Since entry is free, positive short run profit will attract new entry.
(e)
In long run, P = ATC
ATC = TC / Q = (500 / Q) + 50
150 - Q = (500 / Q) + 50
150Q - Q2 = 500 + 50Q
Q2 - 100Q + 500 = 0
Solving this quadratic equation using online solver,
Q = 95 or Q = 5 (Considering integer values only, for output)
When Q = 95, P = 150 - 95 = 55
When Q = 5, P = 150 - 5 = 145
(f)
(i) When Q = 95
TR = 55 x 95 = 5225
TC = 500 + (50 x 95) = 500 + 4750 = 5250
Profit = TR - TC = 5225 - 5250 = - 25 (Loss)
(ii) When Q = 5,
TR = 145 x 5 = 725
TC = 500 + (50 x 5) = 500 + 250 = 750
Profit = TR - TC = 25 - 750 = - 25 (loss)
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