Question

A consumer is 20 years old and expects to live to age 80. He has a current wealth of $100,000, an annual income of $100,000, and plans on retiring when his is 60 years old. Assume he smooths his consumption according to the life-cycle hypothesis. (He does not plan to leave any money to his kids when he dies).

Show an equation that would explain his Annual consumption C
Compute this consumer’s savings in the year when he is 45 years old.
Compute this consumer’s wealth in that same year.
Which if the following would change his annual consumption more:

(1) he wins a $1 million lottery today, or
(2) his annual income is $120,000 (starting today). SHOW why. SHOW all work.

Answer 1

Given Wealth: $100,000 (w)

Annual Income: $100,000 (y)

Equation: Annual Consumption (C)

Annual Consumption (C) = w + Ry/T

Substitute all value in equation

C = 100,000 + (40 × 100,000)/60

C = 100,000 + (4,000,000)/60

C = 4,100,000/60

C = 68333.33

At 45 Years Old:

Annual Saving 68333.33 is spend every year

= 100,000 – 68333.33

= $ 31,667

Then,

= $31,667 × 25

= $791,675

Consumer Wealth

Consumer Wealth = $100,000 + $791,675

Consumer Wealth = $891,675

Annual Consumption More: (i) $1 Million Lottery

C = $1000000 + (40 × 100,000) / 60

C = $1000000 + $4000000 / 60

C = $5000000 / 60

C = $83333.3

Annual Income is $120,000

C = 100,000 + (40 × 120,000)/60

C = 100,000 + 4800000

C = 4900000/60

C = $81,666.6

At 1 million lottery, his consumption is high