2 The budget constraint in three periods 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 perivous period s2 that earned interest at interest rate R, plus labor income y3. These resources are used for consumption c3, there is no saving in period 3. Question 2.1 Write down the three budget constraints for periods t=1,2,3. Hint: Notice that the budget constraint for period 1 is the same as in class. The budget constraint for period 2 is almost the same, only the left-hand side contains not only consumption c2 but also saving. The new constraint is the constraint in period 3 . Question 2.2 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. 2 The budget constraint in three periods 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 perivous period s2 that earned interest at interest rate R, plus labor income y3. These resources are used for consumption c3, there is no saving in period 3. Question 2.1 Write down the three budget constraints for periods t=1,2,3. Hint: Notice that the budget constraint for period 1 is the same as in class. The budget constraint for period 2 is almost the same, only the left-hand side contains not only consumption c2 but also saving. The new constraint is the constraint in period 3 . Question 2.2 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