Question

Consider a hypothetical economy where: • C(Yd) = 105 + 0.8 × (Y − T)

• I(r) = 74 − 1 × r

• G = 65 • T = 50

1. Using the information above, write out the planned Aggregate Expenditure equation.

2. Write down an expression for the Investment-Savings (IS) Curve.

3. Assume that inflation is zero, so that i = r. This economy’s central bank follows a given Monetary Policy Rule: r = i = 0.003 × Y + 0.001 × P where P is the price level. Given this and the expression for the IS Curve, write down an expression for the Aggregate Demand Curve.

4. Suppose that the price level (P) is 1000. What is the equilibrium value of aggregate income, Y ?

5. What are the equilibrium values of the interest rate, r, and investment, I?

6. Suppose that the price level (P) falls to 500. What is the equilibrium value of aggregate income, Y ?

7. What are the new equilibrium values of the interest rate, r, and investment, I?

8. Discuss why the change in the price level has the identified impacts on Y , r and I

Answer 1

Given,

Consumption Function: C(Yd) = 105 + 0.8(Y − T)

Investment: I(r) = 74 − r

Government Spending (G) = 65

Taxes (T) = 50

1. The planned aggregate expenditure is given by the sum of all expenditures in an economy during a specific time period

AE = C + I + G

AE = 105 + 0.8(Y − T) + (74 – r) + 65

AE = 105 + 0.8(Y – 50) + (74 – r) + 65

AE = 105 + 0.8Y -40 + 74 – r + 65

AE = 204 + 0.8Y – r                 ---------------------- Equation 1

2. The Investment Saving Curve (IS) shows all combination of income and interest rates where the goods market is in equilibrium. Here, Aggregate expenditure(AE) is equal to the aggregate output/income (Y)

At equilibrium,

AE = Y

204 + 0.8Y – r = Y

204 – r = Y – 0.8Y

204 – r = 0.2Y

Y = (204/0.2) - (r/0.20)

Y = 1020 – 5r                             ---------------------- Equation 2

3. Given the monetary policy rule : i = r = 0.003Y + 0.001P, we substitute the value of “r “ in equation 1 to find the new aggregate expenditure equation.

AE = 204 + 0.8Y – r       

AE = 204 + 0.8Y – [0.003Y + 0.001P]

AE = 204 + 0.8Y - 0.003Y – 0.001P

AE = 204 + 0.797Y – 0.001P ---------------- Equation 3

4. Given Price level (P) = 1000, the equilibrium is given by :

AE = Y

204 + 0.797Y – 0.001P = Y

204 + 0.797Y – 0.001(1000) = Y

204 + 0.797Y – 1 = Y

203 = Y - 0.797Y

203 = 0.203Y

203/0.203 = Y

Y = 1000

5. Given equilibrium income Y = 1000 and P = 1000

• Equilibrium Interest Rate ( r ) = 0.003Y + 0.001P

                                                     = 0.003(1000) + 0.001(1000)

                                                     = 3 + 1

                                                     = 4%

• Equilibrium Investment ( I ) = 74 – r

                                                 = 74 – 4

                                                 = 70