Question

What is the relationship between the \(M P C\) and the multiplier?

Short answer

The multiplier (K) and the Marginal Propensity to Consume (MPC) are directly related. The multiplier is the reciprocal of 1 minus the MPC. Thus, the larger the MPC, the larger the multiplier and thus, the larger the influence of an increase in spending on the overall economy.

Step-by-step solution

Understanding MPC and Multiplier

Before identifying the relationship, one needs to understand the fundamentals of both the concepts. MPC is the increase in consumer spending due to an increase in income. Therefore, if the MPC is 0.8, that means 80% of additional income is spent on consumption. The multiplier, on the other hand, gives a measure of the impact on GDP from a change in spending.

Discussion on Relationship

The MPC and the multiplier are directly related. A higher MPC means that consumers tend to spend a larger portion of their additional income, which can lead to a higher level of induced expenditure in the economy. This, in turn, increases the multiplier because the initial increase in spending by households can lead to a more than proportionate increase in income and output in the economy.

Establishing the Mathematical Relationship

The multiplier (k) is the reciprocal of 1 minus the MPC. Mathematicaly, it is represented as: \[K = \frac{1}{1-MPC}\] So, the larger the MPC, the larger the multiplier, because a larger portion of the additional income generated in the economy is spent.

Example as Illustration

For example, let's assume that the MPC is 0.8. Using the formula above, we can calculate the value of multiplier as: \[ K = \frac{1}{1 - 0.8} = 5 \] Therefore, an increase in government spending or investment by one unit would lead to an increase in income or output by five times.