Question

Patience has a utility function ?(?1 , ?2 ) = √?1 + 0.8√?2 , where C1 and C2 denote her consumption in periods 1 and 2 respectively. Her income in period 1 is 3 times as large as her income in period 2. At what interest rate will she choose to consume the same amount in period 1 as in period 2?

Answer 1

Assuming U(c1, c2) = c1/21 + 0.80c2/22

Now let interest rate be r

Income saved in period 1 will be equal to (1+r) times in period 2.

Writing utility function in terms of income function

U(I1, I2) = (I1-s)/21 + 0.80(I2+s(1+r))/22

For the same consumption in two periods

0.8(1+r)/22 = 1/21

Solving we get r as = 22/(21*0.8) = 30.9

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