### Utility Function and Expenditure Analysis#### Problem 1: Finding the Expenditure FunctionAn individual has a utility function given by $ U(X, Y) = \min\{4X^2, Y^2\} $. The task is to find the expenditure function as a function of the prices $ p_x, p_y $ and utility $ U $.The options for the expenditure function $ E(p_x, p_y, U) $ are:- a. $ E(p_x, p_y, U) = U(p_x + p_y) $- b. $ E(p_x, p_y, U) = U^2(p_x + 2p_y) $- c. $ E(p_x, p_y, U) = \sqrt{U \left(\frac{p_x}{2} + p_y\right)} $- d. $ E(p_x, p_y, U) = \sqrt{U(p_x p_y)} $The correct answer is:- c. $ E(p_x, p_y, U) = \sqrt{U \left(\frac{p_x}{2} + p_y\right)} $#### Problem 2: Utility Maximization with a Given Expenditure FunctionEugene has the following expenditure function:\[ E(p_x, p_y, U) = p_x^{1/2} p_y^{1/2} U. \]Given that Eugene has an income of 200 and the prices are $ p_x = 1 $, $ p_y = 4 $, we need to determine the maximum utility he can achieve.The options for the maximum utility are:- a. 25- b. 50- c. 100- d. 200The correct answer is:- c. 100#### Explanation of Solution to Problem 2To solve this, we use the given expenditure function:\[ E(p_x, p_y, U) = p_x^{1/2} p_y^{1/2} U. \]Substitute the given values:\[ 200 = (1)^{1/2} (4)^{1/2} U \]\[ 200 = \sqrt{1} \cdot 2 \cdot U \]\[ 200 = 2U \]\[ U = \frac{200

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An individual has utility function U(X, Y) = min{4X2, Y2). Find the expenditure function as a function of prices Px. Py, U. %3D O a. E(p. Py, U = U(px + Py) O b. E(px. Py. U) = U²(p, + 2p,) O c. E(px, Py, U) = VUG + P,) %3D %3D O d. E(px. Py, U) = VU(PxPy) %3D Clear my choice

An individual has utility function U(X, Y) = min{4X2, Y2). Find the expenditure function as a function of prices Px. Py, U. %3D O a. E(p. Py, U = U(px + Py) O b. E(px. Py. U) = U²(p, + 2p,) O c. E(px, Py, U) = VUG + P,) %3D %3D O d. E(px. Py, U) = VU(PxPy) %3D Clear my choice

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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