Final answer:
To find the equilibrium in the closed Keynesian economy, we must set aggregate demand equal to aggregate supply. After solving the provided equations, we can use the equilibrium income to determine the necessary change in government spending to reach a potential GDP of 3,500 using two different methods: directly solving for G and calculating the multiplier effect.
Step-by-step explanation:
The question deals with finding the equilibrium in a closed Keynesian economy and determining the necessary changes in government spending to achieve a potential GDP. Let's address the problem step by step. First, to find the equilibrium, we set aggregate demand equal to aggregate supply (Y = C + I + G + X - M), where Y represents income or output. Using the given equations and plugging in the values:
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- Taxes (T) = 0.25Y
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- Consumption (C) = 400 + 0.85(Y - T)
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- Investment (I) = 300
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- Government spending (G) = 200
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- Exports (X) = 500
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- Imports (M) = 0.1(Y - T)
We can solve for Y to determine the equilibrium income.
To find the change in G required to achieve a potential GDP of 3,500, we can substitute 3,500 for Y in the same aggregate demand equation and solve for G. This is the first method. For the second method, we calculate the multiplier, which is 1/(1 - marginal propensity to consume out of disposable income + marginal propensity to import). Then, we use the multiplier effect to find out how a change in G affects the overall income level, and thus determine the required change in government spending to reach the potential GDP of 3,500. Both methods will guide us to find out how much G needs to increase or decrease to close the gap between current GDP and potential GDP.