Question

A country is closed. It has no government sector, and its aggregate price levels and interest rates are fixed. Furthermore, the marginal propensity to consume is constant and the country's consumption function is as follows: C = 200 + 0.75YD, where YD is disposable income and C is consumption. Assume that planned investment equals 75.

1. If this country's income increased by $10,000, consumption would increase by:

2. Write the AE equation: AE = ____ + ____ YD

3. When real GDP equals $900 unplanned inventory investment is:

4. What is the income–expenditure equilibrium for this country?

5. Holding everything else constant, what is the change to the income-expenditure equilibrium if aggregate wealth decreases by $100?

6. Holding everything else constant, what is the change to the income-expenditure equilibrium if taxes increase by 100? (hint: think about how the change in taxes reduces consumption).

Answer 1

(1) C = 200 + 0.75YD

Note: The country is closed, it has no government sector. It means there is no taxes.

YD = Y -T

=> YD = Y (because there is no taxes)

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MPC = (ΔC / ΔYD) = 0.75.

Country income increases by $10,000.

=> ΔY = 10,000

Since, YD = Y

=> ΔYD = ΔY = 10,000

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MPC = (ΔC / ΔYD)

=> 0.75 = (ΔC / 10,000)

=> ΔC = 0.75 * 10,000

=> ΔC = 7500

Hence, the consumption will increase by $7500

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(2) In closed economy without government,  AE = C + I

=> AE = 200 + 0.75YD + 75

=> AE = 275 + 0.75YD

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(3) AE = 275 + 0.75Y

Because YD = Y

Put Y = 900

=> AE = 275 + 0.75(900)

=> AE = 950.

Unplanned inventory = Y - AE

=> Unplanned inventory = 900 - 950

=> Unplanned inventory = -50.

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(4) At equilibrium, Y = AE

=> Y = 275 + 0.75Y

=> Y - 0.75Y = 275

=> 0.25Y = 275

=> Y = (275 / 0.25)

=> Y = 1100

income–expenditure equilibrium for this country is $1100.

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(5) If aggregate wealth decreases by $100, then the Consumption will fall by $100 at each level of YD.

New consumption function: C = 100 + 0.75YD

AE = C + I

=> AE = 100 + 0.75YD + 75

=> AE = 175 + 0.75YD

=> AE = 175 + 0.75Y

At equilibrium. Y = AE

=> Y = 175 + 0.75Y

=> Y - 0.75Y = 175

=> 0.25Y = 175

=> Y = (175 / 0.25)

=> Y = 700.

income–expenditure equilibrium for this country will decrease from $1100 to $700.

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(6) Now there is taxes of $100,

-> T = $100.

C = 200 + 0.75YD

=> C = 200 + 0.75(Y -T)

=> C = 200 + 0.75 (Y - 100)

=> C = 200 + 0.75Y - 75

=> C = 125 + 0.75Y

AE = C + I

=> AE = 125 + 0.75Y + 75

=> AE = 200 + 0.75Y

.At equilibrium, Y = AE

=> Y = 200 + 0.75Y

=> Y - 0.75Y = 200

=> 0.25Y = 200

=> Y = 200 / 0.25

=> Y = 800

income–expenditure equilibrium for this country will decrease from $1100 to $800.