4. Consider an individual who lives for 2 periods and each period receives a constant income of $y pesos, which every period he can spend on a single consumer good c (you may normalize the price of this good to 1). She can save/borrow using perfect credit markets with the market interest rate of r. Her preferences can be represented by a strictly quasi-concave utility function U (xo, ¤1) = /x3 + Bx{ %3D a) are these preferences additively separable? monotone? convex? b) derive the conditions for utility maximization c) under which conditions on B and r would she choose to borrow in the first period and under which conditions she would choose to save?

4. Consider an individual who lives for 2 periods and each period receives a constant income of $y pesos, which every period he can spend on a single consumer good c (you may normalize the price of this good to 1). She can save/borrow using perfect credit markets with the market interest rate of r. Her preferences can be represented by a strictly quasi-concave utility function U (xo, ¤1) = /x3 + Bx{ %3D a) are these preferences additively separable? monotone? convex? b) derive the conditions for utility maximization c) under which conditions on B and r would she choose to borrow in the first period and under which conditions she would choose to save?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.2P

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Consider a two-period consumption saving model and let f1 and f2 denote the first and secondperiod consumption, respectively. Assume that the interest rate at which the consumer may lend or borrowis 10%. Suppose that a consumer’s utility function is x (f1> f2) = f1 + 20√f2= The consumer first periodincome is L1 = $100 and the present value of her income stream is $330=(a) What is the optimal consumption stream (consumption bundle) of this consumer?(b) Is this consumer borrower or lender? How much does she borrow or lend?(c) What is the effect of a reduction of the interest rate to 5% on the consumer’s optimal first-periodsaving? (Make sure to take into account the effect of the decline in the interest rate on the present value ofthe consumer’s income stream.)
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