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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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E3
![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, x1) = /x³ + Bx?
V
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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39143d27-4ed0-4cb6-a256-365d5c101b35%2Ffe56b505-90f1-4021-a6c6-be3cffef6b3d%2Fo7iipfd_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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, x1) = /x³ + Bx?
V
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?
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