Question

Consider the 2-period household model that you have seen in class. Suppose the household wants to consume equal amounts in both periods. She earns $100 in the first period and $150 in the second period. The interest rate depends on whether she saves or borrows. The interest rate on saving is 1%, while the interest rate on borrowing is 10%. Required:
What is her optimal consumption?

Answer 1

The optimal consumption of the household based on the interest rate on borrowing given will. 124.87.

How to calculate optimal consumption?

From the information given, the following can be gotten:

Y1 = 100

Y2 = 150

Interest rate on savings = 1%

Interest rate on borrowing = 10%

When she saves, the optimal consumption will be:

c1 + c2/1+r = Y1 + Y2/1+r

c1 + c1/1+0.01 = 100 + 150/1+0.01

(1.01 × c1) + c1/1.01 = (1.01 + 150)/1.01

2.01c1 = 251

c1 = 251/2.01

c1 = 124.87

Therefore, the optimal consumption is 124.87.

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