Income and substitution effect - 經濟

學校:ucla

教師:mazzocco

科目:econ11

題目:A consumer has the following utility function: U(X,Y) =XY. Px=2 and Py=2,
the daily income is $32.
a) How many units of X and Y does she consumes each day?
b) Suppose that the price of Y increases to $8. Find his new optimal
consumption bundle.
c) If his income changes in a way that he can achieve exactly his initial
utility level.
How many units of X and Y would he buy?
d) Using your answers from a) to c), find the income and substitution effect
for Y.

我的想法:
前三題我有做對 但是第四題一直做不出答案
前三題答案是
a) X=8 Y=8
b) X=8 Y=2
c) I=64, X=16, Y=4
第四題是Income effect: 2 units, substitution=4 units

我想用第一題找得marshallian demand求income effect
然後再用slutsky equation求substitute effect
但是怎麼算都都跟答案不一樣

謝謝

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