P. 1. Sam and Janet Evening Run the Only Hotel on a Beautiful Southsea Island. Visitors

HOMEWORK #4

P. 1. Sam and Janet Evening run the only hotel on a beautiful SouthSea island. Visitors come from all over the world to vacation on the island, but businesses also use the hotel for conventions. The price elasticities of demand for hotel rooms are believed to be V = 2 for the vacationers and B = 1.2 for business travelers.

(a)What room rates should Sam and Janet charge these different groups if the marginal cost of providing a room is $30 per day? ______.

(b)The market segment with the less elastic demand is charged the (higher, lower) price; the segment with the more elastic demand is charged the (higher, lower) price.

P. 2. The market for plumbing fixtures (mostly sinks) in Egypt is dominated by one large firm, Pharaoh Faucet, Inc., that acts as a price leader. They allow all other plumbing companies (called the competitive fringe) to supply as many fixtures as they want at the existing price, which Pharaoh sets and other firms accept. The market demand, or total demand, for fixtures is given by the equation: QT = 100 – p, where QT is measured in millions of fixtures and p is the dollar price per fixture. The supply of the competitive fringe firms is equal to QF = (2/3)p. Pharaoh’s MC curve is equal to MC = 1.2QL, where QL is the output of the price leader. Total market demand and the supply of the competitive fringe firms are shown on the left-hand panel of the graph below.

(a)Derive an equation that represents Pharaoh’s share of market demand (what is left over after the competitive fringe firms have supplied the product).

(b)Write Pharaoh’s demand as an inverse demand function and derive an expression for its marginal revenue. Draw Pharaoh’s AR and MR curves on the right-hand panel of the figure.

(c)Graph this price leader’s MC curve on the right-hand panel of the graph. Solve for the profit-maximizing quantity of fixtures that Pharoah should sell. Q = ______. What price will Pharoah set for its fixtures? $______.

(d)What will be the total market demand at this price? ______. How much will be supplied by the competitive fringe firms? ______.

(e)If the price set by Pharoah results in economic profits for the competitive fringe firms, what do you think will happen to this industry over time? ______.

(f)Obviously this market is not purely competitive, and so there should be some deadweight loss. Indicate any deadweight losses on the graphs. (Hint: there are deadweight losses in each market segment.) How much is the total deadweight loss?

P. 3. In the textbook, an analysis was provided that showed how advertising can lead to higher costs and higher prices. Can you think of any cases where advertising leads to lower prices paid by consumers? In your answer, consider both prices and search costs as well as the effect that advertising have on the elasticity of demand.

P.4.

P.5.[1]

[1] Point b is not obligatory.