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Suppose the following equations describe the relationship between the long-run shares of spending in GDP and the interest rate (R), measured in decimal fractions (that is, R=0.05 means that the interest rate is 5 percent). Equations: C/Y

∗=0.7−0.2(R−.05) and I/Y
∗=0.2−0.8(R−.05) X/Y
∗=.0−0.95(R−.05) and G/Y
∗=.2 Use algebra to determine the values of the interest rate and the long-run shares of spending in GDP. R=

C percentage =_____%
I percentage =______%
X percentage =_____%
G percentage =_____%

User Badgerr
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1 Answer

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Final answer:

To find the equilibrium GDP, we use the aggregate expenditure formula and then solve for Y to get an equilibrium GDP of 3,200. To reach the potential GDP of 3,500, the government needs to increase its spending by about 45, considering the multiplier effect of 6.67 based on the calculated marginal propensity to consume.

Step-by-step explanation:

The task is to calculate the equilibrium level of GDP for an economy and determine what change in government spending is necessary to achieve a potential GDP of 3,500. To find the equilibrium GDP, we set the aggregate expenditure equal to GDP. Assuming no taxes for simplicity, the aggregate expenditure (AE) function is AE = C + I + G + X - M, where C is consumption, I is investment, G is government spending, X is exports, and M is imports.

Using the provided formulas:

  • Taxes (T) = 0.25Y
  • Consumption (C) = 400 + 0.85(Y - T)
  • Investment (I) = 300
  • Government spending (G) = 200
  • Exports (X) = 500
  • Imports (M) = 0.1(Y - T)

Substitute T, C, and M into AE:

AE = 400 + 0.85(Y - 0.25Y) + 300 + 200 + 500 - 0.1(Y - 0.25Y)

AE = 1400 + 0.6375Y - 0.075Y

AE = 1400 + 0.5625Y

For equilibrium, AE = Y, thus:

1400 + 0.5625Y = Y

Y - 0.5625Y = 1400

0.4375Y = 1400

Y = 1400 / 0.4375

Y = 3200

The economy's equilibrium GDP is 3,200, which is below the potential GDP of 3,500. To achieve the potential GDP, we need to increase government spending. Since every dollar of government spending has a multiplier effect due to the marginal propensity to consume, we can calculate the required change in G.

The multiplier (k) = 1 / (1 - MPC), where MPC = marginal propensity to consume. Here, MPC = 0.85 (after adjusting for taxes), hence k = 1 / (1 - 0.85) = 1 / 0.15 = 6.67.

To increase GDP by 300 (from 3,200 to 3,500), we calculate the change in G as follows:

Change in G = (Required increase in GDP) / k = 300 / 6.67 ≈ 45.

The government needs to increase spending by approximately 45 to achieve the potential GDP of 3,500.

User Parilogic
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