B.3 Marie has preferences over two goods, cake q₁ and bread q2. She chooses quantities to consume soas to best satisfy these preferences subject to the budget constraint p1q1 + P292 y where p₁ andP2 are prices and y is total budget.Suppose that Marie's preferences are represented by utility function u(q1, 92) = 91 + In (bq1 +92)where b≥ 0 is a preference parameter. Assume that p1/bp2 ≥ y/ (P1 - bp2) ≥ 1.(a) Show that Marie's indifference curves are downward sloping and that her weakly preferred setsare convex for all possible values of b.(b) Show that her Marshallian demand for cake gi isYfi (y, P1, P2)1P1-bp2and find her Marshallian demand for bread, f2 (y, P1, P2). Discuss the shape of Engel curvesfor the two goods.(c) Explain why Marshallian demand curves for normal goods slope down. Are there any values ofb for which either cake or bread could be a Giffen good for Marie? Discuss.(d) Find the form of the indirect utility function and expenditure function and hence establishexpressions for the Hicksian demands for the two goods.

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Answered: B.3 Marie has preferences over two…

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section6.A: Indifference Curve Analysis

Problem 3SQP

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