Question

Problem 1.Consider a consumer who lives for two periods. His income in period 1 equals 2000 EUR and his income in period 2 equals 2500, Real interest rate equals 10% a) Use the appropriate diagram to show the consumer's intertemporal budget constraint and his consumption choice, assuming that he is a net lender in period 1 b) How will his consumption decision be affected if the interest rate increases to 20% Answr using the graph from part (a)? Will he be a net lender, net borrower, or we cannot tell? suppose that the real interest rate equals 10%. How will the consumer's consumption decision be affected by an increase in future income by 200 EUR? Will he be a net lender, net borrower, or we cannot tell? Can we say anything about the change in his savings?

Answer 1

a) income In period 1 = eur 2000

income in period 2 = eur 2500

given real interest rate = 10 %

so present value of income in period 1 = 2000 + 2500/1.1

= 2000 + 2272.72

4272.72

future value of income in period 2 = 2000 *1.1 + 2500

= 4700

The inter temporal budget constraint is given by AEB, E is the endowment point .

Assuming he is a net lender , his consumption point will lie to right of point E, ON SEGMENT BE.

b ) If real interest rate increases to 20%, then

present value of income in period 1 = 2000 + 2500/1.2

= 2000 + 2083.33

4083.33

future value of income in period 2 = 2000 *1.2 + 2500

= 4900

since interest rate has increased , the opportunity cost of money's increase , so he will continue to remain a net lender and his consumption will fall

The new inter temporal budget constraint is given by CED and the consumption point will lie on segment EC so consumption will fall.

if real interest rate = 10% and income in period 2 becomes EUR 2700, then

present value of income in period 1 = 2000 + 2700/1.1

= 2000 +2454.54

4454.54

future value of income in period 2 = 2000 *1.1 + 2700

= 4900

The new inter temporal budget constraint is given by DGF where G is the new endowment point.

  He will increase is consumption as his income is both the period is higher.

Whether he remains a net lender or borrower cannot be told. Nothing can be said about the savings also.