Suppose economists observe that an increase in government spending of $10 billion raises the total demand for goods and services by $30 billion.

a. If these economists ignore the possibility of crowding out, what would they estimate the marginal propensity to consume (MPC) to be?
b. Now suppose the economists allow for crowding out. Would their new estimate of the MPC be larger or smaller than their initial one?

b. MPC will be smaller because the MPC relies heavily upon the real (inflation-adjusted) rate of interest.And crowding out causes increase in interest rate. A high rate of interest causes spending in the future to become increasingly attractive due to the intertemporal substitution effect on consumption.

Because a rate increase primarily decreases the present value of lifetime wealth, the consumer relies on becoming a lender to offset this effect. In a two period model, as S(1+r) increases with the interest rate, so does future income[C= -(1+r)c +we(1+r)]. Therefore, every dollar of current income spent by the consumer is 1(1+r) dollars the consumer will not be able to spend in the second period.