Question

Assume the following behavioral equations for a macroeconomy: C-100+9Y. 1-50, T-100 and G-40

(a) Calculate the equilibrium level of output.

Y=100+,94+50

ly: 150 y = 15001 (b) Given the information, calculate the level of consumption that occurs at the equilibrium level of income.

(c) Suppose government spending increases by 100. Calculate the new equilibrium level of income.

Answer 1

The equilibrium level of output is 2800. The level of consumption at the equilibrium level of income is 2185. The new equilibrium level of income after a government spending increase of 100 is 2500.

Step-by-step explanation:

The equilibrium level of output can be determined by setting the aggregate expenditure (AE) equal to national income (Y).

Using the given behavioral equations:

• C = 400 + 0.85(Y - T)
• I = 300
• G = 200
• X = 500
• M = 0.1(Y - T)

We can substitute the values into the equation:

Y = AE = C + I + G + X - M

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

Y = 1400 + 0.75Y - 0.1T

Substituting T = 0.25Y:

Y = 1400 + 0.75Y - 0.1(0.25Y)

Y = 1400 + 0.75Y - 0.25Y

Y = 1400 + 0.5Y

0.5Y = 1400

Y = 2800

The equilibrium level of output (Y) is 2800.

(b) At the equilibrium level of income, we can substitute Y = 2800 into the consumption equation:

C = 400 + 0.85(Y - T)

C = 400 + 0.85(2800 - 0.25(2800))

C = 400 + 0.85(2800 - 700)

C = 400 + 0.85(2100)

C = 400 + 1785

C = 2185

The level of consumption at the equilibrium level of income is 2185.

(c) If government spending increases by 100, we can substitute the new value of G = 300 into the equation to calculate the new equilibrium level of income:

Y = (400 + 0.85(Y - T)) + 300 + 300 + 500 - 0.1(Y - T)

Y = 1400 + 0.75Y - 0.1T + 1100 - 0.1Y

Substituting T = 0.25Y:

Y = 1400 + 0.75Y - 0.1(0.25Y) + 1100 - 0.1Y

Y = 1400 + 0.75Y - 0.25Y + 1100 - 0.1Y

Y = 2500

The new equilibrium level of income (Y) is 2500.