Imagine that the household in our model lives for three periods, t 1,2,3 In period 1, the household starts with financial wealth f1, and labor income y1, which can be used for consumption c1 and saving s1 In period 2, the household uses saving from previous period s1 that earned interest at interest rate R, plus labor income y2 These resources can be used for consumption c2 or saving s2 In period 3, the household uses saving from previous period s2 that earned interest at interest rate R, plus labor income y3 These resources are not used for consumption c3, there is no saving in period 3 1) Write down budget constraints for periods ,2,3 2) Express s2 from the budget constraint for period 3, and substitute it into the budget constraint for period 2 Now express s1 from the budget constraint for period 2 and substitute it into the budget constraint for period 1 Show that what you obtained is one intertemporal budget constraint that equalizes the present discounted value of consumption to the total wealth of the household

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Oct 11, 2024

Imagine that the household in our model lives for three periods, t= 1,2,3. In period 1, the household starts with financial wealth f1, and labor

Imagine that the household in our model lives for three periods, t= 1,2,3.

In period 1, the household starts with financial wealth f1, and labor income y1, which can be used for consumption c1 and saving s1.
In period 2, the household uses saving from previous period s1 that earned interest at interest rate R, plus labor income y2. These resources can be used for consumption c2 or saving s2
In period 3, the household uses saving from previous period s2 that earned interest at interest rate R, plus labor income y3. These resources are not used for consumption c3, there is no saving in period 3

1) Write down budget constraints for periods ,2,3.

2) Express s2 from the budget constraint for period 3, and substitute it into the budget constraint for period 2. Now express s1 from the budget constraint for period 2 and substitute it into the budget constraint for period 1. Show that what you obtained is one intertemporal budget constraint that equalizes the present discounted value of consumption to the total wealth of the household.