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

To begin, I’ll identify the key components of the economy: consumption, investment, and government spending, while accounting for taxes that affect disposable income.
Option by option, consider how the equilibrium output is determined in a simple closed economy with taxes: Y = C + I + G, where C depends on disposable income Yd and Yd = Y − T.
1) Compute C using the given formula and tax: C = 180 + 0.5 Yd, with Yd = Y − T and T = 120. Therefore, C = 180 + 0.5 (Y − 120) = 180 + 0.5Y − 60 = 120 + 0.5Y. This expresses C directly in terms of Y.
2) Sum up autonomous spending: I = 100 and G = 160 are exogenous, so total autonomous spending is 100 + 160 = 260.
3) Total planned expenditure (aggregate demand) as a function of Y is AE = C + I + G = (120 + 0.5Y) + 100 + 160 = 380 + 0.5Y.
Now set equilibrium where output equals aggregate demand: Y = AE = 380 + 0.5Y.
Solving for Y: Y − 0.5Y = 380 → 0.5Y = 380 → Y = 760.
- Option a: 880. This would require a higher multiplier effect or larger autonomous spending, but the derived equation shows Y must satisfy Y = 380 + 0.5Y, so 880 does not satisfy the equilibrium condition.
- Option b: 780. Close to the computed 760, but plugging Y = 780 into the equation yields AE = 380 + 0.5×780 = 380 + 390 = 770, which is not equal to 780, so not equilibrium.
- Option c: 760. This exactly satisfies Y = 380 + 0.5Y, since 0.5×760 = 380 and 380 + 380 = 760, confirming equilibrium occurs at this level of output.
- Option d: 800. If Y = 800, then AE = 380 + 0.5×800 = 380 + 400 = 780, which is less than Y, so the economy would adjust upward or downward? The mismatch shows 800 is not the equilibrium level.
In summary, only Y = 760 balances total spending with output given C, I, G, and T, making 760 the correct equilibrium level of output. All other options fail to satisfy the equilibrium condition Y = C + I + G with the specified components.

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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