1 Problem 1: Rational choice: preferences and budget sets Robinson will live thi

Question

1 Problem 1: Rational choice: preferences and budget sets Robinson will live this period and next period alone on his island. His only income is obtained from picking coconuts. Suppose he collects 100 coconuts this period and 70 coconuts next period. Coconuts not consumed in this period will spoil at the rate of 50%. (a) Draw Robinson's intertemporal budget constraint. (b) What will be his consumption in each period if he regards future consumption as a perfect, one-for-one substitute for current consumption? (c) What will be his consumption in each period if he regards future consumption as a perfect, one-for-one complement of current consumption?

Explanation / Answer

a) Let C1 be the number of coconuts he consumes in the 1st period.

Let S1 be the number of coconuts he saves for the 2nd period in the first period.

Let C2 be the number of coconuts he consumes in the 2nd period.

C1 + S1 = 100

C2 = 70 + 0.5S1 = 70 + 0.5(100 - C1)

So Budget Constraint : C2 + 0.5C1 = 120

If plotted between C2 and C1 axes, it will be a straight line with C2 intercept 120 and C1 intercept 240. (It will be negatively sloped)

b) As future consumption is a perfect one to one substitute for current consumption,

That is, if he forgoes consuption of 1 coconut in current period, he will get the same magnitude of utility he sacrificed by consuming 1 coconut in the future.

But since 50% coconuts will get spoiled, he will not save any coconut for the future.

S1 = 0

So C1 = 100

c) As C1=100, S1 = 0,

C2 = 70

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