Question

2. A consumer is making lifecycle consumption plans for two periods (this year and next year). The consumer's current real income after taxes is $100,000. She knows that her real income after taxes will be $121,000 in next year. She can borrow and lend freely at an annual real interest rate of 10%. Currently, the consumer has no wealth (no money in the bank or other financial assets, and no debts). A) If the consumer wants to consume the same amount of consumption this year and next year, then how much should she consume each period? B) If the consumer wants to consume next year twice as much as the consumption of this year, then how much should she consume each period? Does she borrow or save this year? (hint: if this year consumption is x, the next year consumption is 2x.]

Answer 1

A) Since the consumer wants to consume same amount in both periods:

Total income in two periods= 100,000+121,000=221,000

Consumption in period 1= Consumption in period 2= x

x+x=221000

2x=221000

x= 221000/2= 110,500

Hence, the consumer would consume 110,500 in each period. Since the income is less in the first period, the consumer would borrow in the first period.

B) Consumer wants to consume next year twice as much as the consumption this year:

Total income in two periods= 221,000

Consumption in period 1= x

Consumption in period 2= 2x

Total Consumption in both periods= x+2x= 221000

3x= 221000

x= 221000/3= 73667 approx.

Hence, consumption in period 1= 73667 approx.

consumption in period 2= 2x= 2*73667= 147,334

Since the consumption in period 2 is higher than the income in period 2, the consumer would save this year in order to compensate for the consumption in period 2.