Question

Please give a detailed explanation of the Intertemporal budget constraint
with diagram.

Answer 1

Ans.)

Intertemporal budget constraint is a type of budget constraint that measures the total resources available to an individual for consumption at present and future. The current period is the period one with income equal to Y 1 and consumption equal to C1. On the other hand the other period is referred to as the period 2 with income equal to Y2 and consumption equal to C2.

As the consumer is free to borrow and lend in the market, so the current consumption can be either higher or lower than the current income.

S1 = Y1 - C1

In second period consumption equals the saving including the interest earned on that saving plus the second period income.

C2 = S1(1+r) + Y2

Where r is the real interest rate.

For example for every $1 dollar saved in period 1, the consumer consumes $1.05 in period 2.

If the period one consumption is less than the income, the consumer is Saving and it is greater than zero

If the period one consumption is more than the income, the consumer is borrowing and saving is less than the zero.

Substituting the first equation into the second equation gives,

C2 = (1 + r)(Y1 − C1) + Y2

Rearranging the terms gives,

(1 + r)C1 + C2 = (1 + r)Y1 + Y2

Dividing both sides by 1 + r to obtain,

C1 + C2/(1+r) = Y1 + Y2/(1+r)

The above equation relates the consumption into periods to the income in 2 periods.

If the interest rate is equal to zero the consumption in both the periods equals the income in both the periods.

When the interest rate is greater than zero, the future consumption and income are discounted by a factor of 1 + r. As the consumer earns interest on the income that is saved, future income is worth less than the current income.

The factor 1/(1 + r) is the price of 2nd period consumption in terms of first period consumption.

Below is the graph of consumer's budget constraint in which there are three points marked

At point A, consumer's consumption exactly equals his income.So, the consumer is neither borrowing nor saving.

At point B , the consumer consumes nothing in the first period and saves all the income.

So the second period consumption is:

C2 = (1+r)S1 + Y2

At point C,the consumer consumes nothing in period 2 and borrows in the first period. So, the 1st period consumption is equal to :

C1 = Y1 + Y2/(1+r)

There are many other combinations as well which would lie on the budget constraint of the consumer.