Econ302-hw6-spring11-solutions - Econ302 Homework...

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Econ302 Homework Assignment 6 Solution 1. How can a firm determine an optimal two-part tariff if it has two customers with different demand curves? (Assume that it knows the demand curves.) If all customers had the same demand curve, the firm would set a price equal to marginal cost and a fee equal to consumer surplus. When consumers have different demand curves and, therefore, different levels of consumer surplus, the firm is faced with the following problem. If it sets the user fee equal to the larger consumer surplus, the firm will earn profits only from the consumers with the larger consumer surplus because the second group of consumers will not purchase any of the good. On the other hand, if the firm sets the fee equal to the smaller consumer surplus, the firm will earn revenues from both types of consumers. 2. Elizabeth Airlines (EA) flies only one route: Chicago-Honolulu. The demand for each flight on this route is Q = 500 - P. Elizabeth’s cost of running each flight is $30,000 plus $100 per passenger. a. What is the profit-maximizing price EA will charge? How many people will be on each flight? What is EA’s profit for each flight? To find the profit-maximizing price, first find the demand curve in inverse form: P = 500 - Q . We know that the marginal revenue curve for a linear demand curve will have twice the slope, or MR = 500 - 2 Q . The marginal cost of carrying one more passenger is $100, so MC = 100. Setting marginal revenue equal to marginal cost to determine the profit- maximizing quantity, we have: 500 - 2 Q = 100, or Q = 200 people per flight. Substituting Q equals 200 into the demand equation to find the profit- maximizing price for each ticket, P = 500 - 200, or P = $300. Profit equals total revenue minus total costs, = (300)(200) - {30,000 + (200)(100)} = $10,000. Therefore, profit is $10,000 per flight.
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b. Elizabeth learns that the fixed costs per flight are in fact $41,000 instead of $30,000. Will she stay in this business long? Illustrate your answer using a graph of the dema nd curve that EA faces, EA’s average cost curve when fixed costs are $30,000, and EA’s average cost curve when fixed costs are $41,000. An increase in fixed costs will not change the profit-maximizing price and quantity. If the fixed cost per flight is $41,000, EA will lose $1,000 on each flight. The revenue generated, $60,000, would now be less than total cost, $61,000. Elizabeth would shut down as soon as the fixed cost of $41,000 came due. 300 500 200 250 300 305 400 500 Q P D AC 1 AC 2 Figure 11.6.b c. Wait! EA finds out that two different types of people fly to Honolulu. Type A is business people with a demand of Q A = 260 - 0.4P. Type B is students whose total demand is Q B = 240 - 0.6P. The students are easy to spot, so EA decides to charge them different prices. Graph each of these demand curves and their horizontal sum. What price does EA charge the students? What price does EA charge other customers? How many of each type are on each flight? Writing the demand curves in inverse form, we find the following for the two
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This note was uploaded on 05/25/2011 for the course ECON 302 taught by Professor Toossi during the Spring '08 term at University of Illinois at Urbana–Champaign.

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Econ302-hw6-spring11-solutions - Econ302 Homework...

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