Suppose that a government decides to spend $50 billion building bridges and roads. The government’s purchases of goods and services will directly increase total spending on final goods and services by $50 billion. But as we learned in Chapter 11, there will also be an indirect effect: the government’s purchases will start a chain reaction throughout the economy. The firms that produce the goods and services purchased by the government earn revenues that flow to households in the form of wages, profits, interest, and rent. This increase in disposable income leads to a rise in consumer spending. The rise in consumer spending, in turn, induces firms to increase output, leading to a further rise in disposable income, which leads to another round of consumer spending increases, and so on.

As we know, the multiplier is the ratio of the change in real GDP caused by an autonomous change in aggregate spending to the size of that autonomous change. An increase in government purchases of goods and services is a prime example of such an autonomous increase in aggregate spending.

In Chapter 11 we considered a simple case in which there are no taxes or international trade, so that any change in GDP accrues entirely to households. We also assumed that the aggregate price level is fixed, so that any increase in nominal GDP is also a rise in real GDP, and that the interest rate is fixed. In that case the multiplier is 1/(1 − MPC). Recall that MPC is the marginal propensity to consume, the fraction of an additional dollar in disposable income that is spent. For example, if the marginal propensity to consume is 0.5, the multiplier is 1/(1 − 0.5) = 1/0.5 = 2. Given a multiplier of 2, a $50 billion increase in government purchases of goods and services would increase real GDP by $100 billion. Of that $100 billion, $50 billion is the initial effect from the increase in G, and the remaining $50 billion is the subsequent effect arising from the increase in consumer spending.

What happens if government purchases of goods and services are instead reduced? The math is exactly the same, except that there’s a minus sign in front: if government purchases of goods and services fall by $50 billion and the marginal propensity to consume is 0.5, real GDP falls by $100 billion.