What is the multiplier effect

What is the multiplier effect?

What relationship does the MPC bear to the size of the multiplier?
The MPS? What will the multiplier be when the MPS is 0, 0.4, 0.6, and 1? What will it be when the MPC is 1, .90, .67, .50, and 0?

How much of a change in GDP will result if firms increase their level of investment by $8 billion and the MPC is .80? If the MPC is .67?

The Correct Answer and Explanation is :

The Multiplier Effect and its Relationship with MPC and MPS

The multiplier effect refers to the phenomenon where an initial change in spending leads to a greater overall impact on the economy. It occurs because an initial expenditure (such as investment, government spending, or consumer spending) creates income for others, who then spend a portion of it, creating further income, and so on. The total increase in GDP is larger than the initial spending injection.

The size of the multiplier (( k )) is determined by the marginal propensity to consume (MPC) and the marginal propensity to save (MPS), which are related as follows:

[
k = \frac{1}{1 – MPC} = \frac{1}{MPS}
]

Since ( MPC + MPS = 1 ), the multiplier is inversely related to MPS.

Calculating the Multiplier for Different Values of MPS and MPC

1. When MPS = 0:
   [
   k = \frac{1}{0} = \infty \quad (\text{Theoretical infinite multiplier})
   ]
2. When MPS = 0.4:
   [
   k = \frac{1}{0.4} = 2.5
   ]
3. When MPS = 0.6:
   [
   k = \frac{1}{0.6} = 1.67
   ]
4. When MPS = 1:
   [
   k = \frac{1}{1} = 1
   ]

For different values of MPC:

1. When MPC = 1:
   [
   k = \frac{1}{1 – 1} = \infty
   ]
2. When MPC = 0.90:
   [
   k = \frac{1}{1 – 0.90} = \frac{1}{0.10} = 10
   ]
3. When MPC = 0.67:
   [
   k = \frac{1}{1 – 0.67} = \frac{1}{0.33} = 3.03
   ]
4. When MPC = 0.50:
   [
   k = \frac{1}{1 – 0.50} = \frac{1}{0.50} = 2
   ]
5. When MPC = 0:
   [
   k = \frac{1}{1 – 0} = \frac{1}{1} = 1
   ]

Change in GDP Given an Increase in Investment

The total change in GDP is determined by:

[
\Delta GDP = \text{Multiplier} \times \text{Change in Investment}
]

• If MPC = 0.80, then: [
  k = \frac{1}{1 – 0.80} = \frac{1}{0.20} = 5
  ] [
  \Delta GDP = 5 \times 8 \text{ billion} = 40 \text{ billion}
  ]
• If MPC = 0.67, then: [
  k = \frac{1}{1 – 0.67} = \frac{1}{0.33} = 3.03
  ] [
  \Delta GDP = 3.03 \times 8 \text{ billion} = 24.24 \text{ billion}
  ]

Conclusion

The multiplier effect plays a crucial role in determining how changes in spending impact the overall economy. A higher MPC leads to a larger multiplier, while a higher MPS leads to a smaller multiplier. In practical terms, if firms increase investment by $8 billion and the MPC is 0.80, GDP increases by $40 billion, whereas if MPC is 0.67, GDP increases by approximately $24.24 billion. This concept is fundamental in fiscal policy, as governments and policymakers use it to predict the effects of changes in spending on economic output.