消費者剩餘 - 經濟

來源: 黃貞穎老師考古題

科目: 個經

問題:

Consumer's surplus: A consumer has the utility function

U(x,y) =e^((ln(X)+Y)^1/3)

where X is the good in concern and Y is the money
that can be spent on all other goods. (So the price of Y is normalized to
be 1). The income of this consumer is 100.

(a) (10pts) Derive the demand function of x for this consumer. Make sure that
at every price of x, the consumer always has enough income to buy the amount
of x as indicated by hiss demand function.
(b) (10pts) Calculate the price elasticity of the demand function in (a).
Is it true that the absolute value of the elasticity of the demand decreases
as the amount of x increases?
(c) (10pts) Suppose price of x decreases from 2 to 1. Calculate the change
in consumer's surplus.
(d) (10pts) Suppose price of x decreases from 2 to 1. Calculate the
compensating variation of this price change.
(e) (10pts) Suppose price of x decreases from 2 to 1. Calculate the
equivalent variation of this price change .

目前解出a) x=1/px c) ln2
本身沒有修過微積分，
不太知道要利用現有的條件算出價格彈性跟CV,EV
想請較大家<(_)>


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