(d) Does the monopolist waht to stay l U Assume that a monopolist has TC=3+26Q+1
ID: 1104725 • Letter: #
Question
(d) Does the monopolist waht to stay l U Assume that a monopolist has TC=3+26Q+1Q2 an the market demand is P(Q) 50-2Q. (a) What is the profit-maximizing price and quantity (P,Q)? (b) What is the marginal cost at Q? (c) Calculate the price elasticity of demand at (P,Q*) (use the equation for elasticity, not IEPR). (d) Verify that the IEPR holds. 4. Suppose that a monopolist faces TC- 23+72Q and the market demand is Q(P) = 100P3 (a) Find the marginal cost for the firm. (b) What is the price-elasticity of demand for the de- mand curve? (c) What price should the monopolist set in the market? more or less freedom to (d) Would the monopolist haye raise the price if the de were Q (P)=100m 5. A monopolist faces a demand curve P 50-2Q and initially faces a constant marginal cost MC 18 (a) Calculate the profit-maximizing monopoly quantity and price, and compute the monopolist's total rev- enue and profits at the optimal price. (b) Suppose that the monopolist's marginal cost in- creases to MC = 26. Verify that the monopolist's total revenue goes down. ECON 361 Intermedinta iExplanation / Answer
(4)
Total Cost (TC) = 23 + 72Q
Demand function: Q = 100P-2
(a)
Marginal cost (MC) = dTC / dQ = 72
(b)
Q = 100P-2
Point Price elasticity of demand = (dQ / dP) x (P / Q) = - 200P-3 x (P / 100P-2) = - 2
(c) Q = 100P-2
P-2 = Q / 100
P2 = 100 / Q
P = 10 / Q0.5
Total revenue (TR) = P x Q = 10Q0.5
Marginal revenue (MR) = dTR / dQ = 10 x 0.5 / Q0.5 = 5 / Q0.5
Profit is maximized when MR = MC:
5 / Q0.5 = 72
Q0.5 = 5/72 = 0.0694
Q = 0.0048
P = 10 / 0.0694 = 144
(d) If Q = 100P-4,
Point Price elasticity of demand = (dQ / dP) x (P / Q) = - 400P-5 x (P / 100P-4) = - 4
For previous demand function, absolute value of price elasticity was 2. With changed demand function, absolute value of price elasticity is 4, which means demand has become more elastic with changed demand function. More elastic demand means firm cannot increase price as much as it could have done with earlier demand function, because consumers have become more price sensitive and an increase in price will decrease the quantity demanded (and total revenue) more than before.
NOTE: Only Question 4 has been highlighted, so this has been answered assuming only this requires a solution.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.