Answer to Question #122339 in Macroeconomics for Zemba Siamuleya

Question

The value of the multiplier associated with changes in autonomous spending is given by k.
a) Find the value of the multiplier when MPC=0.50, 0.75 and 0.80.
b) What is the relationship between the value of the multiplier and MPC?
c) Find the change in equilibrium level of output when there is a k10 000 increase in investment spending and MPC=0.50, 0.75 AND 0.80.

Answer 1

a) Find the value of the multiplier when MPC=0.50, 0.75 and 0.80.

The multiplier is calculated as:

$$k = \dfrac{1}{1 - MPC}$$

When MPC = 0.50, the value of the multiplier is:

$$k = \dfrac{1}{1 - 0.50}\\[0.3cm] \color{red}{k = 2}$$

When MPC = 0.75, the value of the multiplier is:

$$k = \dfrac{1}{1 - 0.75}\\[0.3cm] \color{red}{k =4}$$

When MPC = 0.8, the value of the multiplier is:

$$k = \dfrac{1}{1 - 0.8}\\[0.3cm] \color{red}{k = 5}$$

b) What is the relationship between the value of the multiplier and MPC?

From question (a), we can see that as the value of MPC increases, the value of the multiplier increases as well. Thus, there is a direct relationship between the MPC and the value of the multiplier.

c) Find the change in equilibrium level of output when there is a k10 000 increase in investment spending and MPC=0.50, 0.75 AND 0.80.

The multiplier is equal to:

$$\dfrac{\Delta Y}{\Delta I} = \dfrac{1}{1 - MPC}$$

When $\Delta I = 10,000\text{ and } MPC = 0.50$ , then:

$$\dfrac{\Delta Y}{10,000} = 2\\[0.3cm] \Delta Y = 2\times 10,000\\[0.3cm] \color{red}{\Delta Y = 20,000}$$

When $\Delta I = 10,000\text{ and } MPC = 0.75,$ then:

$$\dfrac{\Delta Y}{10,000} = 4\\[0.3cm] \Delta Y = 4\times 10,000\\[0.3cm] \color{red}{\Delta Y = 40,000}$$

When $\Delta I = 10,000\text{ and } MPC = 0.80,$ then:

$$\dfrac{\Delta Y}{10,000} = 5\\[0.3cm] \Delta Y = 5\times 10,000\\[0.3cm] \color{red}{\Delta Y = 50,000}$$