Question

An economy is described by the following equations: (LO3, LO4, LO5) C = 3,000 + 0.5(Y - T) Iᴾ = 1,500 G = 2,500 NX = 200 T = 2,000 Y^* = 12,000 For this economy, find the following: autonomous expenditure, the multiplier, short-run equilibrium output, and the output gap. Illustrate this economy rsquo s short-run equilibrium on a Keynesian-cross diagram. Calculate the amount by which autonomous expenditure would have to change to eliminate the output gap. Suppose that the government decided to close the output gap by reducing taxes. By how much must taxes be reduced in order to do this?

Answer 1

The equations given define an economy's components such as consumption, investment, government spending, net exports, and taxes. By substituting these values into the aggregate expenditure equation, the equilibrium output is determined to be 12,000. The autonomous expenditure, multiplier, short-run equilibrium output, and output gap are then discussed. The output gap is found to be zero, meaning no change in autonomous expenditure is needed to eliminate it. Lastly, the amount by which taxes must be reduced to close the output gap is calculated to be 3,000.

Step-by-step explanation:

The equations given are:

Taxes (T) = 0.25Y

Consumption (C) = 400 + 0.85(Y - T)

Investment (I) = 300

Government spending (G) = 200

Net exports (X) = 500

Imports (M) = 0.1(Y - T)

In order to find the equilibrium for this economy, we need to set aggregate expenditure (AE) equal to national income (Y).

AE = C + I + G + (X - M)

In this case, we have AE = Y.

Substituting the given equations into AE, we get Y = 400 + 0.85(Y - 0.25Y) + 300 + 200 + (500 - 0.1(Y - 0.25Y))

Simplifying the equation, we find that Y = 12,000.

Autonomous Expenditure:

The autonomous expenditure is the part of expenditure that does not depend on income or national income. In this case, C, I, G, X, and M are all autonomous expenditure components. Therefore, the autonomous expenditure is given by C + I + G + (X - M), which is equal to 400 + 300 + 200 + (500 - 0.1(Y - T)).

The Multiplier:

The multiplier measures the change in equilibrium income resulting from a change in autonomous expenditure. The multiplier is calculated as the inverse of the marginal propensity to save (MPS), which is equal to 1/0.1 = 10. Therefore, the multiplier is 10.

Short-run Equilibrium Output:

The short-run equilibrium output is the level of national income where aggregate expenditure (AE) is equal to national income (Y). In this case, the short-run equilibrium output is 12,000.

Output Gap:

The output gap measures the difference between the actual level of output (Y) and the potential level of output (Y*). In this case, the output gap is calculated as Y - Y*, which is equal to 12,000 - 12,000 = 0.

Change in Autonomous Expenditure to Eliminate the Output Gap:

The output gap is zero in this case, indicating that the actual level of output is equal to the potential level of output. Therefore, no change in autonomous expenditure is needed to eliminate the output gap.

Change in Taxes to Close the Output Gap:

To close the output gap by reducing taxes, we need to calculate the amount by which taxes must be reduced. The equation for taxes is T = 0.25Y. To close the output gap, we set Y equal to Y*, which is equal to 12,000. Substituting 12,000 for Y in the equation, we find that T = 0.25(12,000) = 3,000.