Question

Suppose the preferences of an individual are represented by a quasilinear utility func- tion: U (x, y) = 3 ln(x) + 6y (a) Initially, px=1, py=2 and I=101. Then, the price of x increases to 2 (px=2). Cal- culate the changes in the demand for x. What can you say about the substitution and income effects of the change in px on the consumption of x? (Hint: since the change in price is not small, you cannot use the Slutsky equation) (b) What can you say about the substitution and income effects of the change in px on the consumption of y? (c) Instead of doubling to 2, suppose px is only increased by a small amount. Use the Slutsky equation to find the substitution and income effects of the change in the price of x on the consumption of x. Compare your result to (a). Explain why there’s no income effect of the change in px on the consumption of x. Show your result on an indifference curve. (d) Use the Slutsky equation to find the substitution and income effect of the change in px on the consumption of y. Compare your result to (b).

Answer 1

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