1. You are the manager of a New Orleans Cruises line providing service between S
ID: 1148839 • Letter: 1
Question
1. You are the manager of a New Orleans Cruises line providing service between St. Croix and Puerto Rico. New Orleans Cruises’ two 700 guest ships offer an extraordinary service, fine cuisine, and rare experience. Since yours is the only cruise service between these two ports, your firm is a monopoly. The demand for each trip is Q = 2000 – P, the cost of each trip is $500,000 per trip in fixed costs plus $500 per passenger. a. What price should you charge per passenger in order to maximize total revenues? At that price, how many people will be on board? b. What price should you charge per passenger in order to maximize profits? At that price, how many people will be on board? c. Calculate your profits at the profit-maximizing price and quantity. d. If your fixed costs rise to $750,000, will your company stay in business in the short-run? What about the long run? e. Suppose that your company hires an economist to analyze passenger demand. The economist discovers two distinct classed of passengers. The first class is comprised of business travelers who must travel this route for their companies. The demand function for business travelers is QB = 1200 - 0.2PB. The second class is comprised of people on vacation. Their demand function is QV = 800 - .8PV. Also, assume that your company can price-discriminate between the classes of passengers. Using the original cost function, determine the ticket prices for each class of passenger. How many business and vacation travelers will sail on your ship at these prices? 2. Consider the following demand and supply curves: P 20 18 16 14 Q 0 1 2 3 P 2 3 4 5 Q 0 1 2 3 a. What is the equation of this demand function? b. What is the equation of this supply function? c. Solve for equilibrium price and quantity. 3. The market demand and supply for jet fuel is provided by the following functions: Qd = 140 - P Qs = -160 + 4P Where: P= Price per barrel Q= quantity in thousands of barrels If the government imposes a tax of t per unit on quantity supplied and the market adjusts the supply function to include the tax when t = $5/barrel: a. Find the initial equilibrium price and quantity? b. Find the new equilibrium price and quantity after the tax. c. Illustrate with a diagram how this tax will affect the market demand and supply curves. d. Who bears the tax and by how much? 4. Suppose the airline industry is confronted with a 10% increase in the negotiated wages for their pilots but ticket prices remain constant. Explain with the aid of graphs why the airline might not wish to increase its ticket prices.
Explanation / Answer
(1)
Q = 2,000 - P, therefore
P = 2,000 - Q
Total cost, C ($) = 500,000 + 500Q
(a)
Total revenue (TR) = P x Q = 2,000Q - Q2
Revenue is maximized when dTR/dQ = 0
2,000 - 2Q = 0
2Q = 2,000
Q = 1,000
P = 2,000 - 1,000 = $1,000
(b)
Profit is maximized when Marginal revenue (MR) equals Marginal cost (MC).
MC = dC/dQ = 500
MR = dTR/dQ = 2,000 - 2Q
Equating MR & MC,
2,000 - 2Q = 500
2Q = 1,500
Q = 750
P = 2,000 - 750 = $1,250
(c)
When P = $1,250 and Q = 750,
TR ($) = 1,250 x 750 = 937,500
C ($) = 400,000 + (500 x 750) = 400,000 + 375,000 = 775,000
Profit ($) = TR - C = 937,500 - 775,000 = 162,500
(d)
Increase in fixed cost ($) = 750,000 - 400,000 = 350,000
Since increase in fixed cost is higher than profit, firm will not stay in business in long run. However, in short run, since fixed cost does not impact MC, firm will stay in business in short run.
NOTE: As per Chegg Answering policy, first 4 parts are answered.
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