3. (4 points) There are two groups of households in the economy: groups [1] and [2].
Group [1]: High-income families. A large share of their annual income is capital income: earnings on their
financial assets. Because this capital income can fluctuate a great deal from year-to-year, their spending is only
weakly tied to their income. As a result, their mpc is about 0.1. They do not lose jobs in recession; they do not gain
jobs in recovery.
Group [2]: All other families. The vast majority of their income is labor income. They have very low saving
rates. When they lose their jobs, they reduce spending; when they are re-hired, they increase spending. They have
some access to credit, and so do not need to cut their spending $-for-$ when their income is cut. As a result, their
mpc is about 0.8. Jobs that are eliminated or created as part of the business cycle are filled by workers in group [2].
The government can cut taxes for some or all of the high income families. Or it can raise transfer payments for some
or all of the other families. The government cannot do both programs; it must choose. Both programs cost the same
amount: $200 billion per year.
a. Whether the government cuts taxes by $200 billion or increases transfer payments by $200 billion, the initial
effect on disposable income is the same. By how much does disposable income initially change?
b. If the government cuts taxes, by how much will equilibrium income change? Show your work.