[考題 106年清大經濟所]

There are three measures for a consumer’s welfare when the price of a good she consumes changes, namely, compensating variation (CV), equivalent variation (EV) and change in consumer surplus (△CS). A consumer with money income m=100 consumes only one good x and has utility function . If the price of x first increases from 1 to 4, and then decreases back to 1. Then, the consumer gains from the price changes according to CV, loses according to EV, and no change in welfare according to △CS.

[ 解答 ]

個人極大效用決策可表示為，由於只購買單一商品，故所有的所得將會用於消費，則，而間接效用函數為，支出函數為間接效用函數的反函數

(1)價格由1元漲至4元的消費者剩餘，但價格又降回1元，，福利未變動

(2)價格由1元漲至4元的補償變量
，但價格又降回1元，，所以，表示以補償變量的方式計算福利將受損225

(3)價格由1元漲至4元的對等變量，但價格又降回1元，，所以，表示以對等變量的方式計算福利將受益225