Final answer:
To determine the increase in equilibrium GDP from a $300 increase in government spending with an MPC of 0.5 and a tax rate of 0.5, one must calculate the fiscal multiplier and then apply it. The resulting multiplier is 1.3333, indicating that the $300 increase will raise equilibrium GDP by approximately $400.
Step-by-step explanation:
The student's question concerns the impact on equilibrium GDP after a $300 increase in government spending, given a marginal propensity to consume (MPC) of 0.5 and a proportional income tax rate of 0.5. To calculate the change in equilibrium GDP, we need to use the fiscal multiplier concept. The multiplier can be calculated by using the formula:
Multiplier = 1 / (1 - MPC (1 - tax rate))
Given that the MPC is 0.5 and the tax rate is 0.5, the multiplier would be calculated as follows:
Multiplier = 1 / (1 - 0.5 (1 - 0.5)) = 1 / (1 - 0.25) = 1 / 0.75 = 1.3333
With the multiplier now known, we multiply the initial change in government spending by the multiplier to find the change in equilibrium GDP:
Change in GDP = Multiplier × Change in Government Spending
Change in GDP = 1.3333 × $300 = $399.99
Therefore, a $300 increase in government spending will increase equilibrium GDP by approximately $400 when the marginal propensity to consume is 0.5 and the proportional income tax rate is also 0.5.