Question

2. This question relates to the Fisher Intertemporal Consumption Model. Suppose Y1 = 200, Y2 = 250 and r = 0.03. a) Calculate the maximum amount of consumption in periods 1 and 2. Explain why these two values are different. b) Suppose r increases to 0.05, calculate the maximum amount of consumption in periods 1 and 2. Explain intuitively why the consumption values changed. c) Suppose Y1 increases to 300. Use r = 0.03 to answer this question. Explain numerically and intuitively what has happened to the budget constraint.

Answer 1

Suppose Y1 = 200, Y2 = 250 and r = 0.03.

a) Calculate the maximum amount of consumption in periods 1 and 2. Explain why these two values are different.

Intertemporal budget is

C1 + C2/1 + r = Y1 + Y2/1 + r

C1 + C2/1.03 = 200 + 250/1.03

1.03C1 + C2 = 456

Maximum C1 (period 1 consumption) = 456/1.03 (C2 = 0) = 442.7

Maximum C2 (period 2 consumption) = 456 (C1 = 0)  

Interest rate allows the individual to save the entire consumption that is curtailed in period 1 to earn interest income in period 2 so that total income of 450 becomes 456 in period 2 and the same if borrowed in period 1, reduces total consumption in period 1 from 450 to 442.7

b) Suppose r increases to 0.05, calculate the maximum amount of consumption in periods 1 and 2. Explain intuitively why the consumption values changed.

C1 + C2/1.05 = 200 + 250/1.05

1.05C1 + C2 = 460

Maximum C1 (period 1 consumption) = 460/1.03 (C2 = 0) = 446.6

Maximum C2 (period 2 consumption) = 460 (C1 = 0)  

Higher interest rate will give more interest income so C2 is increased to 460. Higher interest rate would encourage individual to enjoy more consumption in period 1 and perhaps save more.

c) Suppose Y1 increases to 300. Use r = 0.03 to answer this question. Explain numerically and intuitively what has happened to the budget constraint.

Intertemporal budget is

C1 + C2/1 + r = Y1 + Y2/1 + r

C1 + C2/1.03 = 300 + 250/1.03

1.03C1 + C2 = 559

Maximum C1 (period 1 consumption) = 559/1.03 (C2 = 0) = 542.71

Maximum C2 (period 2 consumption) = 559 (C1 = 0)  

When first period income is increased Both the intercepts are changed and the budget line shifts out. The period 1 intercept expands exactly by 100 as it is Y1 + Y2/1 + r. The second period consumption does not shift by 100 but by a greater amount which is 100(1 + r).