課程名稱︰個體經濟學二 課程性質︰系必修 課程教師︰黃貞穎 開課學院：社會科學院 開課系所︰經濟學系 考試日期（年月日）︰2016/04/25 考試時限（分鐘）：180分鐘 試題 : Intermediate Microeconomics Midterm April 25, 2016 1.Eva Airlines has two potential types of customers: businessmen and tourists. Both demands are in discrete amount. A business customer is willing to pay up to 10 dollars for the first trip, 10 more dol- lars for the second trip, 10 more dollars for the third trip, 5 more dollars for the fourth trip and 5 more dollars for the fifth trip. For the sixth trip and onward, a business customer is not willing to pay anything more. A tourist customer is willing to pay up to 10 dollars for the first trip, 8 more dollars for the second trip and 6 more dollars for the third trip. For the fourth trip and onward, a tourist customer is not willing to pay anything more. Eva Airlines has zero fixed cost and zero marginal cost. Suppose there are two business customers and one tourist customer. When a customer is in- different between flying or not flying, he goes for flying. (a)(10%) If Eva Airlines cannot perform any form of price discrimination (so it only set a single price per trip), derives the optimal price that maximizes Eva's profit. How much profit does Eva Airlines earn? (b)(10%) If Eva Airlines can perform the first-degree price discrimination, how many trip will each business customer and each tourist customer fly respectively? How much in total will it charge each business customer and each tourist customer respectively? (c)(10%) Suppose Eva Airlines performs the second-degree price discrimination, so it screens customers by providing two packages. Each package con- sists of a number of trips and a take-it-or-leave-it charge. For in- stance, if a package (x, T) is offered, then a customer can pay the total amount T to fly x times. Since Eva Airlines cannot tell apart its two type customers, it decides to offer one package (xB, TB) aimed for business customers and another package (xT, TT) aimed for tourist customers. Customers supposedly will self select. Can Eva Airlines earn as much as its profit from performing the first- degree price discrimination? Explain. (d)(10%) Continue from (c). Now use the theory you have learned from the se- cond-degree price discrimination to derive the optimal amounts of TB, TT, xB and xT. (e)(10%) Suppose Eva Airlines performs the third-degree price discrimination by checking whether any customer has a tourist visa. It can tell apart business and tourist customers. How much will it charge busi- ness customers per trip? How much will it charge tourist customer per trip? How much does it earn in total? 2.Consider two firms (A and B) competing by choosing prices. The mar- ginal cost of both firms are 0. Firm A's price is denoted by pA and firm B's pB. The two firms have some degress of product differentia- tion. Because of brand loyalty, they face the following symmetric demand curves: qA = 2 - pA -r*(pA - pB) when 2 - pA -r*(pA - pB) >= 0 and zero otherwise; qB = 2 - pB -r*(pB - pA) when 2 - pB -r*(pB - pA) >= 0 and zero otherwise. Notice that qA is the quantity demanded of A and qB that of B. r > 0 is a parameter capturing the degree of sub- stitutability of the products of A and B. They play pure strategies. Let us first understand the demand curve of say A, qA = 2 - pA -r*(pA - pB). When r is close to 0, demand reduces to qA = 2 - pA. This cap- tures the situation where two firms face independent demands, i.e. their demands depends on own prices only. On the other hand, when r becomes very large, 2 - pA -r*(pA - pB) will become very negative. Hence quantity demanded of A is zero. Essentially this captures the idea that when they are close substitutes, consumers wants to buy from the cheapest firm. Hence no one buys from the more expensive firm. Thus we learn that when r is larger, the two firms are close substi- tutes. (a)(10%) Suppose they choose prices simultaneously. Solve for firm A's reaction function pA = f(pB) and firm B's reaction function pB = f(pA). Gra- phically illustrate the two reaction functions and determine the equ- librium price in the market. (b)(10%) Continue from (a), when r goes to infinity (implying they are close substitutes), what do pA and pB approach? Argue that this resembles the Bertrand competition we learned in class. (c)(10%) Continue from (a) but now assume that A chooses the price first. After observing the choice of firm A, firm B chooses its price. Graphically illustrate this situation and solve for the prices charged by these two firms. (d)(10%) Continue from (c), when r goes to infinity (implying they are close substitutes), what do pA and pB approach? Compare this with your ans- wer in (b). This confirms what we talk in class that outcomes in se- quential price setting in spirit is similar to outcomes in simultane- ous price setting. (e)(10%) Compare from (a) but now assume that firm A and B form a cartel. Solve for the price charged by these two firms. If firm A believes firm B will keep its price, can firm A increase its profit by decreasing its price or increasing its price? --

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