Question

Is the relationship between changes in spending and changes in real GDP in the multiplier effect a direct (positive) relationship, or is it an inverse (negative) relationship? How does the size of the multiplier relate to the size of the MPC? The MPS? What is the logic of the multiplier-MPC relationship?

Short answer

The changes in spending and the changes in real GDP have a positive relationship in the multiplier effect.

The larger the size of MPC, the larger the multiplier will be, and vice versa.

The larger the size of MPS, the smaller the multiplier will be, and vice versa.

Multiplier and MPC are positively related; the greater the MPC value, the greater the consumption expenditure will be, and, thus, the greater will be the increase in real GDP.

Step-by-step solution

Relationship between the changes in spending and changes in real GDP

A multiplier gives the proportion of change in real GDP due to a unit change in spending.A change in spending induces a change in real GDP. The following formula gives the multiplier effect:

$△\mathrm{Y}=\mathrm{k}△\mathrm{I}$, where k is the multiplier.

The above formula shows that the change in real GDP is positively related to the change in spending. For example, if the change in investment is $2000 and MPC is 0.1, then the change in income will be $200 (2000×0.1).

Relation between the multiplier and the MPC

Since the multiplier is the effect of change in total spending, a larger MPC means greater income generation through private consumption. Therefore, the multiplier has a positive relation with MPC.

Therefore, for the large size of the multiplier, the MPC should be large.

$$\begin{gathered} k=\frac{△Y}{△Spending} \\ k=\frac{△Y}{\left(1-MPC\right)△Y} \\ k=\frac{1}{1-MPC} \end{gathered}$$

Thus, the multiplier is directly related to MPC.

Relation between the multiplier and the MPS

The multiplier effect measures the result of changes in expenditure components on the income. A smaller MPS means larger spending through private consumption and a higher increase in the real GDP. Therefore, the multiplier is inversely related to MPS.

$$\begin{gathered} k=\frac{△Y}{△I} \\ k=\frac{△Y}{MPS\left(△Y\right)} \\ k=\frac{1}{MPS} \end{gathered}$$

Logic for multiplier and MPC relationship

MPC measures the propensity to consume out of a unit increase in income. The greater the value of MPC, the greater proportion of the income will be consumed. Greater consumption expenditure will result in greater demand for goods and services and will encourage firms to increase production and investment. An investment increase will further encourage the demand by distributing higher income in society.

Thus, the increase in GDP is higher than before (when the MPC was smaller). The multiplier effect is greater due to the higher MPC value.