Question

Explain the working of the multiplier.

Short answer

Answer: The multiplier effect is a concept in macroeconomics that demonstrates how an initial change in spending can lead to a larger change in output. It occurs due to the chain of spending initiated by the initial change, which is based on the marginal propensity to consume (MPC). Policymakers use the multiplier effect to estimate the impact of their fiscal policies on economic growth.

Step-by-step solution

Understand Marginal Propensity to Consume (MPC) and Induced Spending

Marginal Propensity to Consume (MPC) is the proportion of an additional unit of income that will be spent on consumption. In other words, it tells us how much of any extra money people earn will be spent. Induced spending refers to the spending that is generated as a result of the initial change in spending.

Understand the basis of the multiplier concept

The multiplier effect occurs because an initial change in spending leads to a chain of spending. For example, when the government spends money on building a new road, this initial spending creates income for construction workers. These workers spend a portion of their income, which generates more income for others, and so on. This chain of spending continues, eventually leading to a larger change in output than the initial change in spending.

Introduce the multiplier formula

The multiplier (k) can be calculated using the following formula: \(k = \frac{1}{1 - MPC}\), where MPC is the marginal propensity to consume. To find the change in output, we can multiply the initial change in spending by the multiplier: \(\Delta Y = k \cdot \Delta I\).

Example - Calculate the multiplier and change in output

Suppose the government increases its spending by $1,000, and the MPC is 0.8. First, we need to calculate the multiplier: \(k = \frac{1}{1 - MPC} = \frac{1}{1 - 0.8} = 5\). Now, we can calculate the change in output due to this increase in spending: \(\Delta Y = k \cdot \Delta I = 5 \cdot 1,000 = 5,000\). Thus, in this case, an initial increase in spending of \(1,000 leads to a total change in output of \)5,000.

Interpret the results

The multiplier effect demonstrates how an initial change in spending can lead to a larger change in output. In our example, a \(1,000 increase in government spending led to a \)5,000 increase in output. The multiplier depends on the marginal propensity to consume; the higher the MPC, the larger the multiplier, resulting in a more significant change in output. This concept is important for policymakers, as it helps them estimate the impact of their fiscal policies on economic growth.