To determine the total increase in spending due to the government's increase in education spending, we will use the concept of the spending multiplier in macroeconomics. Here is a step-by-step solution:
1. Understanding the Problem:
- The government increases education spending by [tex]$30 billion.
- The marginal propensity to consume (MPC) is 0.96.
- We need to find out how much the total spending will increase.
2. Calculate the Spending Multiplier:
- The spending multiplier (k) is derived from the marginal propensity to consume (MPC) using the formula:
\[
k = \frac{1}{1 - MPC}
\]
- Plug in the given MPC of 0.96 into the formula:
\[
k = \frac{1}{1 - 0.96}
\]
- Simplify the denominator first:
\[
1 - 0.96 = 0.04
\]
- Now calculate the multiplier:
\[
k = \frac{1}{0.04} = 25
\]
3. Calculate the Total Increase in Spending:
- The total increase in spending is found by multiplying the initial increase in spending by the spending multiplier:
\[
\text{Total Increase in Spending} = \text{Increase in Education Spending} \times k
\]
- Given the increase in education spending is $[/tex]30 billion, we calculate:
[tex]\[
\text{Total Increase in Spending} = 30 \, \text{billion dollars} \times 25 = 750 \, \text{billion dollars}
\][/tex]
4. Conclusion:
- The total increase in spending due to the government's [tex]$30 billion increase in education spending, given a marginal propensity to consume of 0.96, is $[/tex]750 billion.
- Therefore, the final rounded answer is:
[tex]\[
\boxed{750.0 \, \text{billion dollars}}
\][/tex]
