Final answer:
To calculate equilibrium income, one must set aggregate expenditures (C + I + G + X - M) equal to national income (Y) and solve for Y. Adjustments to government spending can then be made to achieve a certain potential GDP.
Step-by-step explanation:
The student's question revolves around calculating the equilibrium income in a hypothetical economy given certain economic parameters such as consumption, investment, government spending, exports, and imports. To find the equilibrium income, we use the equation Y = C + I + G + (X - M). Taxes (T), consumption (C), investment (I), government spending (G), exports (X), and imports (M) all play a role in this calculation. To see how government spending changes can affect the potential GDP achievement, we either substitute the potential GDP into the equations and solve for G, or calculate the multipliers and use them for the analysis.
To find the equilibrium, we need to solve the equation when aggregate expenditures (AE) are equal to the national income (Y). For that, we set AE = C + I + G + (X - M) and Y = national income and find the value of Y that satisfies the equation. In the given equation, T = 0.25Y, C = 400 + 0.85(Y - T), I = 300, G = 200, X = 500, and M = 0.1(Y-T). After substituting the values and solving for Y, we reach the point of equilibrium. If the potential GDP is 3,500, we can adjust the initial value of government spending to achieve this target.