Barbara allocates her consumption according to the two-period Fisher intertempor

Question

Barbara allocates her consumption according to the two-period Fisher intertemporal choice model. Her first period income is dollar 58,000 and her second period income is dollar 73,000. She can save or borrow at a 5 percent interest rate. In your calculations, you should use percentages in decimal terms, not in integer terms (e.g., 5 percent would be written as 0.05, not 5). Round all answers to the nearest dollar. Suppose that Barbara wants her consumption in the first period to be dollar 61,000. What would her second period consumption be? Suppose that she wants her first period consumption to be as high as possible. What is her maximum possible consumption in the first period? Suppose that she wants her consumption to be equal in both periods (that is, she wants C_1 = C_2). What will her consumption be each period?

Explanation / Answer

a)

C1 = Consumption in 1st period = $61,000

Y1 = Income in 1st period = $58,000

C2 = Consumption in 2nd period

Y2 = Income in 2nd period = $73,000

R = Interest rate = 5% = 0.05

As per Fisher intertemporal choice model,

C1 + C2/ (1+R) = Y1 + Y2/ (1+R)

=> 61000 + C2 / (1+0.05) = 58000 + 73000 / (1+0.05)

=> C2 / 1.05 = 58000 + 69523.80952380952 - 61000

=> C2 / 1.05 = 66523.8095238095

=> C2 = 66523.8095238095 x 1.05 = 69850

So the second period consumption will be $69,850

b) The maximum first period consumption should be 58000 + 69523.80952380952 = 127523.80952381

c) If she wants to split equaly, then 127523.80952381 / 2 = 63761.9047619048

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