# Workshop #4 Problems

Using Aggregate Supply and Demand Models

## Question #1

Assume an aggregate supply curve of the following sort:
P = 1.41 + .0001Y

where P = the average price level and Y = GNP

### 1. Now, derive an aggregate demand function from the following data:

A consumption function in which C = 100 + .9Y d-20P, Yd = Y - T

An investment function in which I = 400 - 40P
Government expenditures, G = 300

Lump sum taxes, T = 100

*Hint: you want an equation in which Y is a function of P.*

### 2. Now that you have aggregate supply and demand curves, solve for the equilibrium level of Y and for the price level.

### 3. Solve for the components of GNP, i.e., C, I and G (to check yourself they should sum to the level of GNP that you found in question #2.

### 4. Now suppose that the government decides to stimulate the economy by raising its expenditures from 300 to 400. What will be the consequences for GNP? for the price level and on the various components of GNP? Will this expansion in government spending have caused any "crowding out" effects on investment? Will the change in the price level have caused the kind of change in consumption expenditures that the consumption function would seem to suggest? If not, what has offset this expected effect?

## Question #2

Assume an aggregate supply curve of the sort:
P = 1 + .00125Y

### 1. Now, derive an aggregate demand function from the following data:

C = 50 + .8Y - 10P

I = 200 - 30P

G = 200

T = 50

### 2. Solve for equilibrium output and equilibrium price level.

### 3. Check the math by calculating C and I, and verifying that Y = C + I + G at equilibrium output.

#### 4. Suppose the government tries to deal with the current deficit by raising taxes from 50 to 100. What will be the effects on Y? on C? on I? Compare the change in consumption spending to the size of the tax increase. Which is greater? Explain this result briefly.