Can some just point into the right direction on how to solve this?
1. Suppose you live four periods and earn income of $30,000, $60,000, and $90,000 in the first three periods, and then retire in the fourth period. Assume the interest rate is 0.
a. Suppose you want to consume the same amount in each period of your life. How much would you consume each period? Indicate in which periods you would save and dissave and in what amounts.
b. Assume now that, contrary to part a, there is no possibility for borrowing (i.e. the credit market is closed to you). Under this assumption, how much will you consume in each period? In answering this question, continue to assume that if possible, an even flow of consumption is preferred. (Note: you are assuming here that there are liquidity constraints.)
c. Assume now that you are still liquidity constrained, but you receive an increase in income of $13,000 in period 1. How will your consumption be affected in each period? Relate your answer to the problem of excess sensitivity of consumption to current income.
To solve this problem, we need to consider income, consumption, savings, and borrowing for each period. Let's break down and answer each part of the question step by step:
a. To consume the same amount in each period, you need to divide your total income evenly across the four periods.
Total income = $30,000 + $60,000 + $90,000 = $180,000
Consumption in each period = Total income / 4 = $180,000 / 4 = $45,000
You would save in the first three periods because your income exceeds your consumption. Since there is no interest rate, you do not earn any return on your savings. The savings and dissavings would be:
Period 1:
Income = $30,000
Consumption = $45,000
Savings = $0
Dissavings = Consumption - Income = $45,000 - $30,000 = $15,000 (dissaving)
Period 2:
Income = $60,000
Consumption = $45,000
Savings = $15,000
Dissavings = $0
Period 3:
Income = $90,000
Consumption = $45,000
Savings = $45,000
Dissavings = $0
Period 4 (retirement):
Income = $0
Consumption = $45,000
Savings = $0
Dissavings = $0
b. If there is no possibility for borrowing, and the credit market is closed, you cannot consume more than your current income in any period. You have to adjust your consumption according to your income. Since an even flow of consumption is preferred:
Period 1:
Income = $30,000
Consumption = $30,000
Period 2:
Income = $60,000
Consumption = $30,000
Period 3:
Income = $90,000
Consumption = $30,000
Period 4 (retirement):
Income = $0
Consumption = $0
c. If you receive an increase in income of $13,000 in period 1, it will affect your consumption in each period. However, as you are still liquidity constrained, you cannot borrow against future income even with the increase.
Period 1:
Income = $30,000 + $13,000 = $43,000
Consumption = $43,000
Period 2:
Income = $60,000
Consumption = $30,000
Period 3:
Income = $90,000
Consumption = $30,000
Period 4 (retirement):
Income = $0
Consumption = $0
The problem of excess sensitivity of consumption to current income is evident in this scenario. Even with an increase in income in period 1, your consumption in periods 2 and 3 remains the same. This suggests that you have a higher marginal propensity to save rather than spend, leading to a lack of responsiveness in consumption to changes in income.