申論題

7. A goods market is described by the following set of equations:
Y = C (Y - T (Y )) + I (r ) + G₀ ,
where Y is the level of national income, and C, I, G, and T are consumption, investment, government
spending, and taxes, respectively. If we denote disposable income as , then the consumption function can be expressed as: , where 1 is the marginal propensity to consume.Investment spending is assumed to be a strictly decreasing function of the rate of interest, r: . The public sector is described by two variables: government spending (G) and taxes (T). Typically, government spending is assumed to be exogenous whereas taxes are assumed to be an increasing function of income:
0 < T ''(Y ) < 1.
A money market is described by the following three equations: , , and
, where 0 and the money supply is assumed to be exogenously determined by the central monetary authority.

(c) Derive the following two comparative-static derivatives: