The Math behind the Aggregate Expenditures Model Exercise 3 Your research into a

Question

The Math behind the Aggregate Expenditures Model Exercise 3 Your research into a nation has yielded the following information Autonomous expenditure (A)-$300 Gross investment (I) $200 Government purchases (G) $300 Net exports (NX)-$225 Taxes (T) $300 MPC 0.75 Instructions: Use a negative sign () when necessary a. Substitute the values above into the equation: AE-A [MPC (Y T+1+G+NX Then aggregate expenditures (AE) b. Knowing that AE Y at the equilibrium level of output, what is the equilibrium level of ou Ye 3200 C c. What is the tax multiplier for this economy? 4 d If taxes decrease by $40, from $300 to $260, what is the new equibrium level of outp Ye [3320 O e. With this new tax level of $260, the government will: ® not tax businesses enough e collect more in taxes than they spend on government purchases @spend more on government purchases than they collect in taxes have enough tax revenue to pay for all their imports

Explanation / Answer

(a)

AE = A + [MPC * (Y - T)] + I + G + NX

AE = 300 + [0.75 * (Y - 300)] + 200 + 300 + 225

AE = 300 + 0.75Y - 225 + 200 + 300 + 225

AE = 800 + 0.75Y

The AE equation is as follows -

AE = 800 + 0.75Y

(b)

At equilibrium,

AE = Y

800 + 0.75Y = Y

Y - 0.75Y = 800

0.25Y = 800

Y = 800/0.25 = 3,200

The equilibrium level of output (Ye) is $3,200.

(c)

MPC = 0.75

Calculate the Tax Multiplier -

Tax multiplier = -MPC/(1-MPC)

Tax multiplier = -0.75/(1-0.75) = -0.75/0.25 = -3

The Tax Multiplier in the economy is -3.

(d)

Taxes decreases by $40.

When taxes decreases, income and output increases.

Increase in output = Tax multiplier * Decrease in taxes = (-3) * (-$40) = $120

New equilibrium level of output = Original equilibrium level of output + Increase in output = $3,200 + $120 = $3,320

The new equilibrium level of output (Ye) is $3,320.

(e)

New tax level is $260. Government purchases is $300.

Government purchases is greater than the new tax level.

This means that government will spend more on government purchases then they will collect in taxes.

Hence, the correct answer is the option (3).

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