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25 September, 10:52

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]

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  1. 25 September, 10:56
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    Y = AE = 5,106.38

    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
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