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黃貞穎 08考古題

科目:

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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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