Recall the IS-LM model from your intermediate macro course.1In particular, the goods-market equilibrium condition (GMEC) wasY=C(YT)+I(r)+G, and the money-market equilibrium condition (MMEC) wasm=L(r, Y). Here, the exoge- nous variables areG(government spending),T(taxes), andm(real money supply). The endogenous variables areY(output, or income) andr(real interest rate).C()is the con- sumption function, which is increasing in disposable incomeYT, but less than one-for-one (i.e.,0< C<1).I()is the investment function, which is decreasing inr(i.e.,I<0).L(,)is the demand function for real money balances, which is decreasing inr, and increasing inY(i.e.,Lr<0,LY>0).

(a)Totally differentiate the GMEC, allowing all variables (endogenous and exoge- nous) to potentially vary.

(b)Totally differentiate the MMEC, again allowing all variables (endogenous and exogenous) to potentially vary.

(c)For given values of the exogenous variables, the IS curve is defined as the combinations ofYandrthat put the goods market into equilibrium; that is, it's the solution curve for the GMEC. Find the slope of the IS curve (i.e., finddr/dYfor it). Determine the sign of this slope.2(HINT: We are holding the exogenous variables in the GMEC constant here, and allowing only the endogenous ones to vary. Use this fact to simplify your answer from (a), and then solve it fordr/dY.)

(d)For given values of the exogenous variables, the LM curve is defined as the combinations ofYandrthat put the money market into equilibrium; that is, it's the solution curve for the MMEC. Using steps analogous to part (c), find the slope of the LM curve (i.e., finddr/dYfor it). Determine the sign of this slope.

(e)Recall that (short-run) equilibrium occurs when both the goodsandmoney markets are in equilibrium, i.e., when both equilibrium conditions hold simultaneously. LetYandrdenote these short-run equilibrium quantities ofYandr. Replacingdr=dranddY=dYin your answers to (a) and (b), solve for changes in the endogenous variables (dranddY) explicitly in terms of changes in the exogenous variables (dG,dT, anddm).

(f) Using your answers from (e), find the impact of an increase inGon the equi- librium, holding the other exogenous variables constant (i.e., finddY/dGanddr/dG). Determine the signs of these derivatives.

(g) Using your answers from (e), find the impact of an increase inTon the short- run equilibrium, holding the other exogenous variables constant (i.e., finddY/dTanddr/dT). Determine the signs of these derivatives.

(h)Using your answers from (e), find the impact of an increase inmon the short- run equilibrium, holding the other exogenous variables constant (i.e., finddY/dmanddr/dm). Determine the signs of these derivatives.