We use the following terminology in this part: aggregate income Y and disposable income Yd (= (1−t)Y ), consumption function C(Yd), planned investment function I(r), government spending G, and taxation T = tY where t is the marginal tax rate; r% denotes the real interest rate in the economy. (Note, r is in percentage points, e.g. r = 2 means the interest rate is 2%. When doing calculations, the interest rate should not simply be inserted in decimal form. For example, if r = 5 then I(5) = 52 − 0.2 × 5 = 51.) Consider a hypothetical economy where: C(Yd) = 58 + 0.6 × Yd I(r) = 52 − 0.2 × r G = 180 t = 0.4 (represents 40%)
1. Using the information above, write out the planned Aggregate Expenditure equation. (Hint: Remember that this takes the form of AE = . . . .) Answer: AE = 290 + 0.36Y - 0.2r
2. Write down an expression for the Investment-Savings (IS) Curve. (Hint: First use the AE equation to find an expression for equilibrium Y . Next, remember that the IS equation takes the form of r = ....) Answer: r = 1450 - 3.2Y
3. Assume that inflation is zero, so that i = r. This economy’s central bank follows a given Monetary Policy Rule: r = i = 0.02 × Y + 0.05 × 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. (Hint: Remember that the AD Curve takes the form P = . . . .) Answer: P = 29,000 - 64.4Y
4. Suppose that the price level (P) is 20. What is the equilibrium value of aggregate income, Y ? (Hint: use the AD equation.) Answer: Y = 450
5. What are the equilibrium values of the interest rate, r, and investment, I? (Hint: use the MP R or IS, and I(r) equations.)
Need help with question 5. Based on the above information, what is the answer for question 5?