2. Jie's preference is represented by the utility function U(x,y) = x0.5y0.5, where xand y are two kinds of commodities with price p, and py. Jie's income is 10, andPx = Py = 1. Now because of policy, the price of commodity x increases to 2, theequivalent variation is%3Dand the compensating variation is3. Jie has a utility function of the form U(x, y) = max {3x + 2y, 4x + y}. Initially bothgood x and good y cost $1. Then the price of x increases to $2, the change of demandwith respect to good y due to substitution effect isand the change dueto income effect is4. Jie consumes two goods x and y in two periods 1 and 2. His utility function isU(x1, y1, X2, y2) = (Vx1 +y1)(VX2+ y2). The prices for goods x and y are 2 and 4,respectively, and prices do not change over time. Jie's earnings in period 1 and period2 are both 2. The interest rate is 10%, and debt is not allowed. Then the deposit afterperiod 1 (no interest still) would beand he would consume (x1, y1) =in period 2.in period 1 and (X2, y2) =.4

We are going to find Compensating and Equivalence variation to answer this question. Note: As per…

2. Jie's preference is represented by the utility function U(x, y) = x0.5y0.5, where x and y are two kinds of commodities with price p, and py. Jie's income is 10, and Px = Py = 1. Now because of policy, the price of commodity x increases to 2, the %3D equivalent variation is and the compensating variation is

2. Jie's preference is represented by the utility function U(x, y) = x0.5y0.5, where x and y are two kinds of commodities with price p, and py. Jie's income is 10, and Px = Py = 1. Now because of policy, the price of commodity x increases to 2, the %3D equivalent variation is and the compensating variation is

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

2. Jie's preference is represented by the utility function U(x,y) = x0.5y0.5, where x
and y are two kinds of commodities with price p, and py. Jie's income is 10, and
Px = Py = 1. Now because of policy, the price of commodity x increases to 2, the
equivalent variation is
%3D
and the compensating variation is
3. Jie has a utility function of the form U(x, y) = max {3x + 2y, 4x + y}. Initially both
good x and good y cost $1. Then the price of x increases to $2, the change of demand
with respect to good y due to substitution effect is
and the change due
to income effect is
4. Jie consumes two goods x and y in two periods 1 and 2. His utility function is
U(x1, y1, X2, y2) = (Vx1 +y1)(VX2+ y2). The prices for goods x and y are 2 and 4,
respectively, and prices do not change over time. Jie's earnings in period 1 and period
2 are both 2. The interest rate is 10%, and debt is not allowed. Then the deposit after
period 1 (no interest still) would be
and he would consume (x1, y1) =
in period 2.
in period 1 and (X2, y2) =.
4

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