題組內容

2. Let Y and r denote output and the real interest rate, respectively, in a Keynesian closed economy with the following specifications:

\( \succ \) Desired consumption: \( C^d = 10 + 0.8(Y - T) - 30r \)
\( \succ \) Desired investment: \( I^d = 40 - 20r \)
\( \succ \) Government purchases: \( G = 30 \)
\( \succ \) Taxes: \( T = 40 \)
Full-employment \( (FE) \) output: \( \bar{Y} = 182.5 \)
\( \succ \) Nominal money supply: \( M = 600 \)
Real money demand: \( L = 20 + 0.8Y - 200(r + \pi^e) \)
Expected inflation rate: \( \pi^e = 0.1 \)

(3) Suppose the government aims to restore the economy to its long-run equilibrium, where $\bar{Y} = 182.5$, while the price level remains fixed at P = 5. For each of the following policy scenarios, compute the required policy value separately and illustrate your answers in the IS-LM-FE diagram. (15%)
a. With M = 600 and T = 40 unchanged, what level of government purchases (G) is required?
b. With M = 600 and G = 30 unchanged, what level of taxes (T) is required?
c. With T = 40 and G = 30 unchanged, what level of nominal money supply (M) is required?