來源: (例如: XX 年度高考, XX 年度研究所考) 黃貞穎 08考古題 科目: 個經 問題: Ding Ding (DD) is a male cat who likes only two goods, apples and oranges. Apples and oranges can only be consumed in discrete amount. DD’s master, Jun-Yi, follows the suggestion of DD’s vet closely. Jun-Yi is thinking hard about how to feed DD to make DD happy. DD’s inborn preference is "budget-set-dependent". That is, his preference, unlike what we talked about in class, changes when budget set changes. Let us write a daily consumption bundle of DD by (a, o ) where the first element is the amount of apples and the second element is the amount of oranges. DD’s preference is as follows. Given a budget set, he will first calculate the mean bundle of all bundles in the budget set. For any bundle, he calculates the Euclidean distance between the mean bundle and that bundle. The utility of that bundle is then the negative of the distance. For instance, if DD is given the budget set consisting of only 3 bundles (1, 2), (3, 4), (5, 6), then the mean bundle of all bundles in the budget set is (1+3+5 /3 , 2+4+6 /3 ) = (3, 4). So given this budget set, the utility of consuming bundle (1, 2) is - 8^0.5 since the distance between (1, 2) and the mean bundle (3, 4) is __________________ √(1-3)^2 + (2- 4)^2 = √8. Suppose the price of orange is 1 and Jun-Yi plans to spend at most 3 dollars on DD every day. (a) (15 points) When the price of apple is 1, if the vet suggests that Jun-Yi should offer all bundles that at most 3 dollars can buy and let DD choose whatever he likes the best. In a diagram, draw the budget set and the indifference curves of DD in this situation. (b) (5 points) List all the optimal bundle(s) in (a). (c) (15 points) Now suppose the vet suggests that Jun-Yi should offer all bundles that at most 3 dollars can buy with an additional constraint that DD should at least have 2 oranges every day to get enough vitamin C. In a new diagram, draw the new budget set and the new indifference curves of DD in this situation. (d) (5 points) List all the optimal bundle(s) in (c). (e) (20 points) Is DD’s utility higher in (b) or in (d)? No matter what your answer is, do you think it makes sense to compare DD’s utility in (b) to his utility in (d)? Briefly explain. (f) (20 points) If the vet suggests that Jun-Yi should offer all bundles that at most 3 dollars can buy and let DD choose whatever he likes the best. Imagine that the price of apple can be either 1, 2, or 3. Draw the price offer curve of DD for these three prices. Accordingly, draw the demand curve for apples of DD for these three prices. 我的想法: budget set會是一堆點 同時無異曲線會是同心圓 很詭異的題目 (e)要我們比較時，會發現貓咪很會自打嘴巴 讓我完全失去信心的是(f)的demand curve 點!點!點!點!點! 希望不是我漏看題目關鍵敘述@@" --

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