Final answer:
The equilibrium GDP is found by setting aggregate expenditure equal to GDP and solving the equation. To achieve a potential GDP of 3,500, we need to adjust government spending by either plugging the value directly into the AE equation or by calculating the multiplier effect.
Step-by-step explanation:
To find the equilibrium GDP for this closed Keynesian economy, one can set aggregate expenditure (AE) equal to GDP (Y). We calculate AE using the formulas provided.
AE = C + I + G + X - M, with consumption (C) being dependent on after-tax income (Y - T), where T represents taxes. Plugging in the given values and the tax rate, we have:
AE = 400 + 0.85(Y - 0.25Y) + 300 + 200 + 500 - 0.1(Y - 0.25Y).
Simplifying this equation to solve for Y, we find the equilibrium GDP.
To determine the change in government spending (G) needed to achieve a potential GDP of 3,500, we follow two methods:
- Substitute 3,500 for Y in the AE equation and solve for the new G.
- Calculate the multiplier effect using the marginal propensity to consume (MPC) and the marginal tax rate (t) to determine the change in G that would boost GDP to 3,500.
Both methods should yield the requisite change in G needed to reach the desired potential GDP.