#macroeco

The lower the real interest rate, the _____ the amount of investment.

Consider a two period model: present and future.

Consumption in the present period is given as ct and consumption in the future period id given as cf

Income in the present period is given as yt and income in the future period id given as yf

Let r be the real rate of interest.

Unexpected increase in transitory income:

The consumption of present period will increase. However to have smooth consumption across all periods, consumption increases by a little in present and a little in the future.

Saving also increases in the present period.

The transitory shock is transferred to future.

The budget constraint will shift parallel to the right which implies that the consumer enjoys a higher utility.

Unexpected increase in permanent income:

Consumption in the present period will increase. Consumption in the future period will also increase. Increase in consumption in both the periods will be much more than in the transitory case.

Saving in the present period will remain constant.

Therefore consumption shall move one to one with income.

Both present and future income has increased so the budget constraint shifts parallel out. This implies a higher utility level, even higher than the case of a transitory increase. Therefore households respond more to permanent shocks to income. Transitory shocks increase saving.

Unexpected one time increase in wealth (say a bequest):

This is equivalent to a onetime transitory increase in income.

Consumption will increase both in present and the future.

Saving will fall in present.

Recessions:

Consumption does not vary a lot with temporary income changes. This is called the excess sensitivity of consumption.

Recessions have a little effect on the lifetime income

Households will maintain a saving to buffer the low income (temporary) during recessions.

Liquidity constraints:

When the present income falls and people have no saving and are in no position to borrow, then consumption will fall.

The effect of an increase in the real interest rate:

In case the person is a net borrower then consumption in present will fall while saving in present period shall rise. However the effect on future consumption is ambiguous.

In case the person is a net saver then future consumption will rise but the effect on present consumption and present saving is ambiguous.

The effect of lowering of income tax: