Answer to Question #193219 in Macroeconomics for Ndapewa

Question #193219

Given consumption = 100 +0.75Yd

Tax = 50 + 0.5Y

Export = 200

Import = 50 + 0.25Y

Government spending = 150

Investment = 200

a) Determine the equilibrium level of income/output

b) Illustrate aggregate spending and equilibrium level of income on a diagram      


1
Expert's answer
2021-05-16T19:22:50-0400

"Solution"

"Given \\ that:"

"Y = C + I + G + X \u2013 M\\\\\n\nC = 100 + 0.75(Y \u2013 T) = 100 + 0.75(Y \u2013 (50 + 0.5Y) = 100 + 0.75Y \u2013 37.5 \u2013 0.375Y\\\\\n\nI = 200\\\\\n\nG = 150\\\\\n\nX \u2013 M = 200 \u2013 (50 + 0.25Y) = 150 \u2013 0.25Y\\\\\n\nY = 100 + 0.75Y \u2013 37.5 \u2013 0.375Y + 200 + 150 + 0.25Y\\\\\n\nY = 100 + 200 + 150 \u2013 37.5 + 0.75Y + 0.25Y \u2013 0.375Y\\\\\n\nY = 412.50 + 0.625Y\\\\\n\nY \u2013 0.625Y = 412.50\\\\\n\n0.375Y = 412.50\\\\\n\nY = \\frac{412.50}{0.375} \n\u200b\t\n = 1100\\\\\n\n\n\nY = 1100\\\\\n\nThe\\ equilibrium\\ level \\ of\\ income\\ or\\ output: Y = 1100"


[B] Aggregate spending and equilibrium level of income on a diagram  .



-Equilibrium is reached when the aggregate expenditure(AE) equals the total amount of output (Y)that is Y=AE. The equilibrium point is where the black line intersects with the green line.

-Aggregate spending/ expenditure is shown by the green line.


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