An individual has a fixed wealth (W) to allocate between consumption in two peri

Question

An individual has a fixed wealth (W) to allocate between consumption in two periods (C1 and C2). The individual’s utility function is given by:
U(C1, C2)
And the budget constraint is:
W=C1+(C2/1+r)
Where r is the one-period interest rate.
a. Show that in order to maximize utility given this budget constraint, the individual should choose C1, and C2 so that the MRS (of C1 for C2) is equal to 1+r.
b. Show that dC2/dr =0 but the sign of dC1/dr is ambiguous. If dC1/dr is negative, what can you conclude about the price elasticity of demand for C2?
c. How might your analysis of this problem be amended if the individual received income in each period (Y1 and Y2) such that the budget constraint is given by
Y1-C1+((Y2-C2)/(1+r))=0?

Explanation / Answer

dC2/dr =0

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