Indicate the equilibrium level of output in an economy where: C = 180 + 0.5 Yd I = 100 G = 160 T = 120

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BlackTom AI · Accepted Answer

We start by restating the problem: determine the equilibrium level of output Y given C = 180 + 0.5 Yd, I = 100, G = 160, T = 120, and with Yd = Y − T.

Option a: 780. To test whether 780 is the equilibrium, we would substitute into the equilibrium condition Y = C + I + G. First express consumption in terms of Y: Yd = Y − T = Y − 120, so C = 180 + 0.5(Y − 120) = 180 + 0.5Y − 60 = 120 + 0.5Y. Then total spending = C + I + G = (120 + 0.5Y) + 100 + 160 = 380 + 0.5Y. Setting Y = 380 + 0.5Y gives 0.5Y = 380 → Y = 760. Since 780 ≠ 760, Y = 780 cannot be the equilibrium.

Option b: 800. Using the same substitution, the equilibrium condition requires Y = 380 + 0.5Y, yielding Y = 760. Therefore 800 does not satisfy the equilibrium condition and is not the correct equilibrium output.

Option c: 880. Again, plug into the same equation: Y must equal 380 + 0.5Y, which implies Y = 760. The value 880 fails the equilibrium condition for this simple model, so it is incorrect.

Option d: 760. With Y = 760, we check consistency: Yd = 760 − 120 = 640, so C = 180 + 0.5(640) = 180 + 320 = 500. Then C + I + G = 500 + 100 + 160 = 760, which exactly equals Y. This confirms that 760 satisfies the equilibrium condition Y = C + I + G.

Synthesis: the only value that satisfies the equilibrium relation Y = C + I + G, given the tax T and the consumption function, is Y = 760. Each of the other options fails to satisfy the equality when substituted back into the model, illustrating the internal consistency required for equilibrium in this simple closed-economy framework.

Indicate the equilibrium level of output in an economy where: C = 180 + 0.5 Yd I = 100 G = 160 T = 120

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