Question

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      

Answer 1

$$Solution$$

$Given \ that:$

$Y = C + I + G + X – M\\ C = 100 + 0.75(Y – T) = 100 + 0.75(Y – (50 + 0.5Y) = 100 + 0.75Y – 37.5 – 0.375Y\\ I = 200\\ G = 150\\ X – M = 200 – (50 + 0.25Y) = 150 – 0.25Y\\ Y = 100 + 0.75Y – 37.5 – 0.375Y + 200 + 150 + 0.25Y\\ Y = 100 + 200 + 150 – 37.5 + 0.75Y + 0.25Y – 0.375Y\\ Y = 412.50 + 0.625Y\\ Y – 0.625Y = 412.50\\ 0.375Y = 412.50\\ Y = \frac{412.50}{0.375} ​ = 1100\\ Y = 1100\\ The\ equilibrium\ level \ of\ income\ or\ output: Y = 1100$

[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.