Rita has the following quasilinear utility function: U(q1,92) = q,0.5 + q2. Suppose that the price of good 1 is 3 and that the price of good 2 is 34. If Rita's optimal bundle includes a positive amount of both goods, then her income has to be bigger than

Rita has the following quasilinear utility function: U(q1,92) = q,0.5 + q2. Suppose that the price of good 1 is 3 and that the price of good 2 is 34. If Rita's optimal bundle includes a positive amount of both goods, then her income has to be bigger than

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Rita has the following quasilinear utility function: U(q,.42) = q,0.5 + a2. Suppose that
the price of good 1 is 3 and that the price of good 2 is 34.
If Rita's optimal bundle includes a positive amount of both goods, then her income
has to be bigger than
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Suppose the utility function of U(x1, x2) = x11/2x21/2 and the budget constraint of p1x1+p2x2=m. Let’s assume that p1=$1.5, p2=$2, and m=$60. Find the optimal bundle. Also, specify the optimal bundle.
A consumer’s preferences over pizza (x) and steak (y) are given by u(x,y) = x2y (HINT: MUx = 2xy and MUy = x2) and his income is I = $120 and py = $1. (a) Calculate his optimal bundle when pX = $8 (call this bundle A) and separately when pX = $1 (call this point C). (b) Finding the decomposition bundle B, calculate the income and substitution effects on the amount of pizza of a decrease in the price of pizza from pX = $8 down to pX = $1. (c) Forget about the decomposition bundle and the two effects. In (a), the price of pizza decreases, hence the agent ends up better off. Let’s quantify how much “better off” the agent becomes after this price drop, in dollars. For this, instead of the price drop, suppose the agent is given some money $m and he optimize utility with this additional gift included to his budget. What should m be, so that his optimal utility with his expanded budget is exactly equal to his utility at the bundle C (the bundle he chooses optimally when pizza price drops to…