Consider the following consumer’s problem: max u(c1 ) + βu(c2) c1c2 subject to c1 + s1 = y1 c2 = y2 + (1 + r)s1 u(c)={1/(1-1/σ}c1-1/σ a) Describe all equations using economic terminology. b) Derive the intertemporal budget constraint for this consumer. c) Set the Langrangean for this problem.
Consider the following consumer’s problem: max u(c1 ) + βu(c2) c1c2 subject to c1 + s1 = y1 c2 = y2 + (1 + r)s1 u(c)={1/(1-1/σ}c1-1/σ a) Describe all equations using economic terminology. b) Derive the intertemporal budget constraint for this consumer. c) Set the Langrangean for this problem.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider the following consumer’s problem:
max u(c1 ) + βu(c2)
c1c2
subject to
c1 + s1 = y1
c2 = y2 + (1 + r)s1
u(c)={1/(1-1/σ}c1-1/σ
a) Describe all equations using economic terminology.
b) Derive the intertemporal budget constraint for this consumer.
c) Set the Langrangean for this problem.
d) Find the first order conditions for a maximum.
e) What is the effect of an increase in the interest rate on savings? Show in equation and explain.
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