(Simple Spending Multiplier) Suppose that the MPC is 0.8, while investment, government purchases, and
net exports sum to $500 billion. Suppose also that the government budget is in balance.
a. What is the sum of saving and net taxes when desired spending equals real GDP? Explain.
b. What is the value of the multiplier?
c. Explain why the multiplier is related to the slope of the consumption function.
I need to know how to work it out but also including the answer
What is the sam of savings and net taxes when desired spending equals to real GDP? Explain.
To answer these questions, we will need to understand the concept of the spending multiplier and the relationship between desired spending, real GDP, saving, and net taxes.
a. What is the sum of saving and net taxes when desired spending equals real GDP? Explain.
The spending multiplier tells us how changes in spending can affect overall output or GDP in the economy. It is calculated as the reciprocal of the marginal propensity to save (MPS), which is the portion of additional income that individuals save rather than spend.
In this case, we are given that the marginal propensity to consume (MPC) is 0.8. The MPS is equal to 1 - MPC, so the MPS is 0.2.
To calculate the spending multiplier, we use the formula:
Multiplier = 1 / MPS
Therefore, the spending multiplier is:
Multiplier = 1 / 0.2 = 5
When desired spending equals real GDP, this means that aggregate expenditure is equal to aggregate income. Since income can be divided into consumption (C), saving (S), and net taxes (T), we can express this as:
Real GDP = C + S + T
Given that the government budget is in balance, government purchases (G) must equal net taxes (T). Therefore, we can rewrite the equation as:
Real GDP = C + S + G
To get the sum of saving (S) and net taxes (T), we rearrange the equation:
S + T = Real GDP - C - G
b. What is the value of the multiplier?
As calculated earlier, the value of the multiplier is 5.
c. Explain why the multiplier is related to the slope of the consumption function.
The consumption function represents the relationship between disposable income (Yd) and consumption (C). It shows how individuals spend their income. The slope of the consumption function represents the marginal propensity to consume (MPC), which is the change in consumption resulting from a change in income.
The multiplier is related to the slope of the consumption function because it shows the magnified effect of changes in spending on the overall economy. When individuals receive additional income, they spend a portion of it, increasing consumption. Higher consumption leads to higher aggregate demand, which in turn increases output and income. This increase in income leads to further increases in consumption, creating a multiplier effect.
The multiplier is equal to 1/MPS, which means that a larger MPC (a steeper slope of the consumption function) results in a higher multiplier. This is because a higher MPC implies that a larger portion of additional income is spent, driving the multiplier effect and increasing the overall impact on GDP.