1. An airline with monopoly power faces a demand with constant elasticity of -2.
ID: 1116667 • Letter: 1
Question
1. An airline with monopoly power faces a demand with constant elasticity of -2.0. It has a constant marginal cost of $20 per unit and sets a price to maximize profit. If marginal cost should increase by 25%, would the price charged also rise by 25%?
2. A monopolist can produce at a constant average (and marginal) cost of AC = MC = 5. It faces a market demand curve given by Q = 53 - P. Calculate the profit-maximizing price and quantity for this monopolist. Calculate its profits.
3. Assume DirectJet is the only airline serving JFK-MCO market. DirectJet estimated that the own-price elasticity of demand for its product is -4.5 and its advertising elasticity of demand is 1.5. Assuming these elasticities are constant, what fraction of the firm’s revenues should the firm “reinvest” in advertising to maximize profits?
4. Perfect competition, given P=$100 TC(Q) = 50 –10Q+ 1/2 Q2 Optimal Price? P=$100 Optimal Output? MR = P = $100 and MC = -10 +Q -10+Q =100 Q = 110 units Maximum Profits? Profit =PQ - C(Q) = (100)(110) - (50-10*10 +1/2*1102) = Profit =110,000-6,000=104,000
5. Given estimates of P = 10 - Q C(Q) = 6 + 2Q a. Optimal output? MR = 10 - 2Q MC = 2 10 - 2Q = 2 Q = 4 units b. Optimal price? P = 10 - (4) = $6 c. Maximum profits? PQ - C(Q) = (6)(4) - (6 + 8) = $10
Explanation / Answer
(1)
Lerner Index (LI) = - 1 / Elasticity of demand = (P - MC) / P Where P: Price, MC: Marginal cost. Therefore,
LI = - 1 / - 2 = 1/2
1/2 = (P - 20) / P
P = 2P - 40
P = $40
When MC rises by 25%, new MC = $20 x 1.25 = $25
Since elasticity remains unchanged, LI remains unchanged.
1/2 = (P - 25) / P
P = 2P - 50
P = $50
Increase in price = ($50 / $40) - 1 = 1.25 - 1= 0.25 = 25%
Therefore, as MC rises by 25%, Price also rises by 25%.
NOTE: As per Chegg answering guidelines, first question is answered.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.