We use the following terminology in this part: aggregate income Y and disposable income Yd (= Y − T ), consumption funct

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We use the following terminology in this part: aggregate income
Y and disposable income Yd (= Y − T ), 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)=30+2/3×(Y −T) I(r) =
52 − 0.2 × r G = 160 t = 0.4 (represents 40%)
- Using the information above, write out the planned Aggregate
Expenditure equation. (Hint: Remember that this takes the form of
AE = . . . .)
- 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 = ....)
- 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
+ 0.04 × 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 = . . . .)
- Suppose that the price level (P) is 50. What is the
equilibrium value of aggregate income, Y ? (Hint: use the AD
equation.)
- What are the equilibrium values of the interest rate, r, and
investment, I? (Hint: use the MPR or IS, and I(r) equations.)
- Suppose that the level of Government expenditure increases to
G = 180. What is the equi- librium value of aggregate income, Y ?
(Note: you will no longer get a round number for Y.)
- What are the new equilibrium values of the interest rate, r,
and investment, I?
- Discuss why how the increase in G impacts Y , r and I in the
context of the ideas of fiscal stimulus, spending multipliers, and
crowding-out.