Question

An Economic Model of National Income in a Closed Private Economy in the Short Run

(We are assuming for this model that there is no trade, no government, and no business saving.)

C = 280 + 0.80*Y        Consumption Function [$Billion/year]

I = 620                         Planned Investment (Purchase of new capital goods and services) [$Billion/year]

Y                                 National Income [$Billion/year]

Part 1. What is the aggregate expenditure function in this model?

Part 2. Suppose firms expect to sell, and produce, 4725 $B worth of goods and services. There would be an unplanned change to inventories. What is the size of this unplanned change and how would you predict that firms would respond to this unplanned change in inventories?

Part 3. What are the equilibrium levels of GDP, Consumption, and Savings in this model?

Part 4. Find the value of the expenditure multiplier in this economy.

Part 5. If investment increases from 620 to 660, find the new equilibrium level of GDP.

Answer 1

C = 280+0.80Y

I = 620

Part 1. Aggregate Expenditure function : AE = C + I

AE = 280+0.80Y + 620

AE = 900 + 0.80Y

Part 2 =

Equilibrium level of GDP :

Y = C + I

Y = 280+0.80Y + 620

0.20Y = 900

Y = 4500 ($ billion )

Equilibrium level of income/ output is $4500 billion . Here planned aggregate Expenditure = planned aggregate supply

Now firm plans to sell and produce $4725 billion worth of goods and services.

Which means that AD < AS

This would mean that producer are willing to produce more than what Household are willing to consume.

Actual inventory level is more than the equilibrium level of inventory by $4725 - $4500 = 225 billion dollar.

Here producers suffer loss due to unsold stock.

In order to achieve equilibrium level of output, they must cut Production .

Part 3. Equilibrium level of gdp = $4500 billion

Consumption = 280 + 0.80 ( 4500) = 3880 billion dollar

At equilibrium savings = investment = $620 billion

Part 4. Expenditure multiplier = 1/(1-MpC) = 1/(1-0.80) = 1/(0.20) = 5

Part 5. ∆I = 40

Multiplier = 5

∆Y = ?

Multilplier = ∆Y/∆I

5 = ∆Y / 40

∆Y = 200

New equilibrium level of gdp = 4500+200 = 4700 billion $