Exercises · 3. Spending, the Multiplier, and the Paradox of Thrift

Exercises

Problems to check your understanding of this chapter. The solutions are folded away — try them yourself first.

Medium

1Medium

In an economy with MPC $c = 0.75$ , the government raises spending by $20$ .

Find the multiplier and the total rise in income, and also the cumulative rise after the first three rounds.

The Multiplier: Spending That Echoes

The expenditure line shifted with

c = 0.75

and

20

of extra spending.

Show solution

The multiplier is $\frac{1}{1 - 0.75} = 4$ , so the total rise in income is $20 \times 4 = 80$ .
The rounds run $20$ , $15$ , $11.25$ , and the first three sum to $46.25$ — a little over half of the total $80$ . The rest trickles in over later rounds, thinner each time.

Hard

2Hard

In an economy where investment is income-sensitive ( $I = 20 + 0.1Y$ , $c = 0.8$ , income currently $420$ ), every household cuts its spending by $6$ .

What happens to income and to realized saving?

The Paradox of Thrift: When Everyone Saves, No One Does

The equilibrium shift under a thrift shock of

6

with income-sensitive investment.

Show solution

The multiplier is $\frac{1}{1 - 0.8 - 0.1} = 10$ , so income falls by $6 \times 10 = 60$ , from $420$ to $360$ .
Investment falls from $62$ to $56$ , and realized saving follows it down from $72$ to $66$ . The attempt to save $6$ more ends with the economy saving $6$ less.