Intertemporal Budget Constraints Intertemporal Budget Constr

Intertemporal Budget Constraints:

Intertemporal Budget Constraints. Consider someone who is planning their consumption and savings over the next T periods. Denote the person\'s income in period t by ye; denote the perso consumption in period t by ct; and denote the person\'s bank balance in period t by be. If the consumer has be 0 dollars in her bank account in period t, then she gets (1 +r)bt dollars in period t +1, where r 0. If bt is negative, then the consumer is borrowing from her bank in period t, and she has to repay (1 +r) bt dollars in period t 1. In each period t T, consumption and bank balances must satisfy (15) t-1 (a) We want to compute the budget c Suppose that bo br 0. Show that yt (16) t-1 (1 r) (1 +r) Hint: Start with the equation yu ci by, and keep substituting be 1-tr 1-+T (b) The above shows how someone\'s total lifetime income is related to her total lifetime consumption Now, we want to see how someone\'s bank balance is related to how she managed her budget in all earlier periods. Let se th ct be the consumer\'s budget surplus at date t. If st 0, then the consumer earned more than she spent; if st 0, then the consumer spent more than she earned Show that (17) st-k (1 r

Solution

According to the \"Oxford Dictionary of Economics,\" an intertemporal budget constraint is \"the requirement that the total spending of an individual, firm, or government must be within the funds available to it over some long period.\"

For an individual, an intertemporal budget constraint is straightforward. An individual\'s budget is constrained by the amount they earn or expect to earn in their lifetime plus the value of any assets they possess. If you sold all of your assets and added that money to the amount you are likely to make in your lifetime that would be your spending limit or intertemporal budget constraint.

Complications can arise with intertemporal budget constraints because of economic uncertainty. This is true for individuals as well as governments and corporations. Because no one can adequately predict economic factors such as unemployment and interest rates, especially over the long term, and because no one can predict when an unforeseen crisis may arise, predicting actual income over extended periods is difficult.

The Intertemporal Budget Constraint -

Co is consumption at time o

C1 is the consumption at time 1

Y0 is the income at time 0

Y1 is the income at time 1

The idea behind the intertemporal budget constraint is to determine what are the combinations of consumption in period 0 and 1 that may be achieved with Y0.

The nominal price of consumption is stamped with price 1 so to speak.

If the use 1 unit of income at time 0 to 1 purcahse consumption at time 0 ,she receive 1 unit of consumption.

if she want to use 1 unit of income at time 0 to purchase consumption at time 1 ,the situation is more complecated ,She does not directlypurchase units of C1 at time 0,Rather she save a unit of income at time 0, and at time 1 she use these savings to consume.

When she save 1 unit of income at time 0, what do she receive at time 1?

In other words ,when she save 1 unit of income ,she will have the unit of income plus the interest on it.

Therefore,she can use a unit of Y0 of consume 1+r units of C1, but this means that in order to consume 1 unit of c1, its constraint her 1/1+r unit of Y0