Question

Imagine the economy is defined by the consumption function of C = 200 + 0.9 (Yd) where 200 is autonomous consumption, 0.9 is marginal propensity to consume, and Yd is disposable income (after taxes) and Yd=Y-T, where Y is national income (or GDP) and T=Tax Revenues=0.3Y (0.3 is the avg. income tax rate). Find the macro equilibrium using the following equation Y = C + I + G + (X - M) where C=200 + 0.9(Yd), I=600, G=1000, X=600, M=0.1Y. What is the equilibrium for this economy? [Remember Y=AE]

Answer 1

Y = AE = 5,106.38

Step-by-step explanation:

C = 200 + 0.9 (Yd) ...................................................... (1)

T = 0.3Y

Yd = Y - 0.3Y .................................................................... (2)

Substitute equation (2) into equation (1) we have:

C = 200 + 0.9 (Y - 0.3Y) = 200 + 0.9 (0.7Y) = 200 + 0.63Y ............. (3)

Y = C + I + G + (X - M) ..................................................(4)

Substituting all the relevant values into equation (4) which is the macro equilibrium using the following equation, we have:

Y = 200 + 0.63Y + 600 + 1,000 + (600 - 0.1Y)

Y = 200 + 0.63Y + 600 + 1,000 + 600 - 0.1Y

Y = 2,400 + 0.53Y

Y - 0.53Y = 2,400

0.47Y = 2,400

Y = 2,400 / 0.47

Y = 5,106.38

Therefore, Y = AE = 5,106.38