1Cobb-Douglas utility maximizationGiven the two-good Cobb-Douglas utility function:И(х, у) — хау1-а ,where 0 < a < 1, px and p, denote the prices of goods x and y, respectively, and M denotes theconsumer's income:Write down the general inequality condition representing the consumers' budgetconstraint.(a)(b)Derive the consumer's optimality condition MRSxy = Px/Py at which the consumer'sutility is maximized and solve the resulting expression for px.Substitute the expression derived in part (b) into the budget constraint derived in part (a)to derive the consumer’s (Marshallian) demand function for good y.(c)(d)Using the result from part (c), derive the consumers’ (Marshallian) demand function forgood x. Show that the demand functions for goods x and y are homogenous of degreezero.Assume p, = 1, py = 2, and M = 10. How much of goods x and y will the consumerdemand? Graph your answer on a well-labeled budget constraint/indifference curvediagram, and be sure to appropriately demark the vertical and horizontal intercepts of thebudget constraint.(e)

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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 8 Note: This question is similar to end-of-chapter problem 3.2 and it is restated here in a multiple choice format. For a utility function for two goods to be strictly quasi-concave (i.e. convex indifference curves), the following condition must hold: UxxU²x - 2UxyUxUy + UyU² 0: the function is strictly quasi- concave. O Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx, Uyy, Uxy > 0: the function is not necessarily strictly quasi-concave. Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx = Uyy = 0, Uxy > 0: the function is strictly quasi- concave. O Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx = Uyy = 0, Uxy < 0: the function is not strictly quasi-concave. Question 10 Note: This question is similar to end-of-chapter problem 3.5a and it is…

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