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

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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%)
1. Using the information above, write out the planned Aggregate
Expenditure equation. (Hint: Remember that this takes the form of
AE = . . . .)
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 = ....)
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
+ 0.04 × 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 = . . . .)