Michael has the utility function u(x, y) = √x + √y. Michael's preferences are strongly increasing and strongly convex. You don't need to show this. (a) Compute the expenditure minimizing demands for x and y as functions of utility u and prices. (b) Compute the CV when prices and income change from (Px. Py, 1) = (10,10,10) to (5,20,20).

Michael has the utility function u(x, y) = √x + √y. Michael's preferences are strongly increasing and strongly convex. You don't need to show this. (a) Compute the expenditure minimizing demands for x and y as functions of utility u and prices. (b) Compute the CV when prices and income change from (Px. Py, 1) = (10,10,10) to (5,20,20).

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter21: The Theory Of Consumer Choice

Section: Chapter Questions

Problem 2CQQ

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A consumer has the following utility function: Ulx, y) = xy -y, *21 where x and y represents the quantities consumed of goods X and Y. y 20 What will be the substitution and income effects for X and Yassuming that the consumer attempts to maintain the same level of utility achieved before price of Y increased (that is, when price of Y was $1)? SEx= +0.5 IEx = -0.5 SE, = -0.25 IE- = -0.25 SEx= +0.293 IE = -0.293 SEy = -0.414 IE, = +0.414 SEr= +0.25 IE SE, = -0.75 IE, = -0.75 = -0.25 SEx= +0.414 IEx = -0.414 SEy = -0.293 IE, = -0.207 Income = $3 Px= $1, Py= $2
5. Consider a consumer whose utility function isu(x,y) = sqrt(xy) (MRS(x,y)=y/x)a. Assume the consumer has income $120 and initially faces the prices px = $1 and py = $1. Howmuch x and y would they buy? Draw the budget constraint and the demands. b. Next, suppose the price of x were to increase to $2. How much would they buy now? Draw thisin the same figure.c. Decompose the total effect of the price change on demand for x into the substitution effect and theincome effect. That is, determine precisely how much of the change is due to each of thecomponent effects. (Hint: See the lecture notes for the two properties that determine the locationof “z”, the reference point for distinguishing the income and substitution effects.)
3. Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 5A/4B³/4. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method. b. Suppose Pa increase. Show graphically the income, substitution effect and total effect and explain. c. Suppose PA increase. Show the graph for CV and EV and explain.
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