課程名稱︰個體經濟學一 課程性質︰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）︰2017/11/06 考試時限（分鐘）：180 試題 : 1. Pete is a five-year-old. His mom, Melody, is a sweets lover and feeds Pete with chocolates and ice cream. Denote (c,i) a bundle which has c pieces of chocolates and i boxes of ice cream. Since Melody only gives Pete finite choices, following what we leared from "GARP for Kids: On the Development of Rational Choice Behavior," in American Economic Review 2001, we say Pete directly reveals he prefers bundle x' to bundle x when he chooses x' over x or over a bundle z which has at least as much of every good as in x, and has more than x in at least one good. We say Pete indirectly reveals that he prefers bundle x' to bundle x when some sequence of directly preferred relations between bundles connect x' to x. (a) (8%) Explain, by giving an example why we need to use this different definition of directly revealed preference. You may need to use Figure 1 taken from the paper. https://i.imgur.com/0WDytuY.png (b) (8%) On Monday, Melody gave Pete choices between (5,1) and (3,3), Pete went for (5,1). On Tuesday, Pete chose (2,4) over (6,1). On Wendnesday, Pete went for (3,3) instead of (2,5). Does Pete directly reveal that he prefers (3,3) to (2,4)? Explain. (c) (8%) Continue from (b) above. Do Pete's choices satisfy the weak axiom of revealed preference? Explain what WARP is first and then your answer. (d) (8%) Continue from (b) above. Do Pete's choices satisfy the strong axiom of revealed preference? Explain what SARP is first and then your answer. (e) (8%) Continue from (b) above but assume instead on Monday, Pete went for (3,3). Pete's choice on Tuesday and Wednesday remain the same. Can you rationalize Pete's choices with a specific preference? Explain. 2. Mars is a very wise monkey. It knows that to survive, it first has to get enough calories from foods to meet basic needs. When that is satisfied, it goes after the taste foods can provide as a gourment. Fang-Chen is the master of Mars. She feeds Mars monkey chows and grapes. They are measured in continuous amount. Monkey chows are particularly rich in calories. Grapes are low in calories. In particular, every monkey chow provides 4 units of calories. Every grape provides 1 unit of calorie. Denote a consumption bundle by (c,g) where c is the amount of monkey chows and g is the amount of grapes in the bundle. Hence the total calories of the bundle is 4c+g. Monkey chows and grapes are both tasty, the total taste of a bundle (c,g) is given by cg. Mars needs at least 100 units of calories as the basic needs. Its preference is as follows. For any two bundles, if the total calories a bundle is at least 100 and that of the second bundle is strictly less than 100, it prefers the former to the latter. If the total calories of both bundles are strictly less than 100, it prefers the one giving higher calories (and is indifferent if both bundles give equal calories). If the total calories of both bundles are at least 100, it prefers the one with better taste (and is indifferent if both bundles are equally tasty). Fang-Chen loves Mars so much that whenever she goes to the local market, she maximizes Mars' preference given her budget constraint. If you will draw in your answers, label monkey chow on the X-axis, grapes on the Y-axis. (a) (10%) Fang-Chen goes to the market and finds that both the price of monkey chows and that of grapes are 1. With m dollars at hand, if Fang-Chen temporarily ignores the basic needs of 100 units of calories and just considers maximizing the total taste, what bundle Fang-Chen will choose for Mars? (b) (10%) Continue from (a) above. Of course, in reality, Fang-Chen cannot ignore the basic needs of 100 units of calories. Calculate the total calories of the bundle in your answer to (a). Determine a bound of money say m' such that when m is lower than this bound, the total calories are less than 100 and hence Fang-Chen needs to adjust her choice. On the other hand, when m is higher than this bound, the total calories are more than 100 and hence it is OK that Fang-Chen ignores the basic needs of 100 units of calories. (c) (10%) Continue from (b) above. Let us now figure out what Fang-Chen should do when m is lower than m'. For that, we first look at the case where m is lower than 25. Derive the optimal choice in this case. Explain briefly. Are monkey chows normal or inferior in this case? (d) (10%) Continue from (c). Let us look at the second case where m is higher than 25 but still lower than m'. First find the bundle on the budget line which gives exactly 100 units of calories. Explain in details why this bundle is the optimal choice. Are monkey chows normal or inferior in this case? (e) (10%) Take what you have leared so far, can you find a price of monkey chows which is higher than 1 so that when the price of monkey chows increases from 1 to this higher price (holding the price of grapes fixed at 1), the demand of monkey chows increase? Explain in details how you get your answer. (f) (10%) We learn that the utility function is a nice convenient way to represent preferences but it is not unique. Can you write down a utility function of Mars? Or do you think Mars' preference cannot be represented by any utility function? Explain. (Hint: You need to pay particular attention to the fact that for any two bundles, if the total calories of a bundle is at least 100 and that of the second bundle is strictly less than 100, Mars prefers the former to the latter.) --

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