1. Consider the utility function given by u (x1, x2) = x1x%, and budget constraint given by Pixi + P2x2 = w. (a) Solve the EMP to find the Hicksian demand function, h (p, u). (b) Find the expenditure function e (p, u). (c) Recover h (р, и) from e (p, и). (d) Noting that the indirect utility function corresponding to the UMP for this form is 4w3 v (P1, P2, w) = demonstrate that v (.) and e (.) are inverses of each other. 27p1p (e) Using only the indirect utility function above, recover the optimal consumption bundle of the UMP (i.e., Walrasian demand function). (f) Using your answer to (e), identify the substitution effect on the quantity demanded of good 1 of a change in the price of good 1. (g) Assume p2 = 1; and consider the Hicksian demand curve for good 1 corresponding to 8 and VWalrasian demand curve for good 1 corresponding to u – 1 At what nrice

1. Consider the utility function given by u (x1, x2) = x1x%, and budget constraint given by Pixi + P2x2 = w. (a) Solve the EMP to find the Hicksian demand function, h (p, u). (b) Find the expenditure function e (p, u). (c) Recover h (р, и) from e (p, и). (d) Noting that the indirect utility function corresponding to the UMP for this form is 4w3 v (P1, P2, w) = demonstrate that v (.) and e (.) are inverses of each other. 27p1p (e) Using only the indirect utility function above, recover the optimal consumption bundle of the UMP (i.e., Walrasian demand function). (f) Using your answer to (e), identify the substitution effect on the quantity demanded of good 1 of a change in the price of good 1. (g) Assume p2 = 1; and consider the Hicksian demand curve for good 1 corresponding to 8 and VWalrasian demand curve for good 1 corresponding to u – 1 At what nrice

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose an individual has the following utility function: U(X,Y)= min{X, 2Y}, and they choose marshallian demands gx,gy. Suppose you have an increase in px. Which of the following is true about the change in demand for good X, gx? (a) No substitution effect, because they only consume one of the goods. (b) No substitution effect, because they always consume the goods in fixed proportion. (c) No income effect, because they only consume one of the goods. (d) No income effect, because they always consume the goods in fixed proportion. Which of the following production functions exhibits constant returns to scale? (a) f(k,l) = 0.310.7 (b) f(k, l) = kl (c) f(k, 1) = ln(k)+ln(1) (d) f(k, l) In(k) + In(1) =
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