According to the life-cycle/permanent-income hypothesis, consumption depends on the present discounted value of income. An increase in the real interest rate will make future income worth less, thereby reducing the present discounted value and reducing consumption. To incorporate this channel into the model, suppose the consumption equation is given by

Assume the remainder of the model is unchanged from the original setup, as in Table 11.1.
(a) Derive the IS curve for this new specification.
(b) How and why does it differ from the original IS curve?

TABLE 11.1 The Setup of the Economy for the IS Curve Endogenous variables: Y C I G EX, IM National income identity: Consumption: Exports: Imports: Investment: Exogenous variables parameters. Yr 7, c, ar r et' ain' b Exogenous for now (until next chapter): R