Question

1. (26 marks total) Math Review: Recall the IS-L.M model from your intermediate macro course In particular, the goods-market equilibrium condition was Y-C(Y-T)+I (r) +G, and the money-market ecluilibrunn condition was m = L (r, Y). Here, the exogenous variables are G government spending), T (taxes), and m (real money supply). The endogenous variables are Y (output, or income) and r (real interest rate). C() is the consumption function, which is increasing in disposable income Y-T, bit less than one-for-one (ie, 0 < C" < 1). 1(.) is the investment function, which is decreasing in r (i.e, I'< 0). L( is the demand function for real balances, which is decreasing in r, and increasing in Y e., L<0, Ly >0). Recall that short-run equilibrium occurs when both the goods and money markets are in equilibrium. Let Y and denote these short-run equilibrium quantitites of Y and r Using total differentiation, answer the following. In each case, if possible, determine the sign of the relevant derivatives, and if it's not possible, explain why (a)(4 marks) The IS curve is the combinations of Y and r that put the goods market into equilibriun. Find the slope of this cuve (i.e., find dr/dY for the IS curve) (b) (4 marks) The LM curve is the combinations ofY and r that put the money market into equilibrinm. Find the slope of this curve (i.e., find dr/dY for the LM curve) (c) (6 marks) Find the impact of an increase in G on the short-run equilibriue, dY /dG and dr dG) (d) (6 marks) Find the impact of an increase in T (i.e., dY./dT, and drソdT) e) (6 marks) Find the impact of an increase in m (i.e., dY"Idm and dr/dm)

Answer 1

Consider the given problem here the goods market eqn is given by y = c(y - T) + I(x) + G� where c'(middot) elementof (0, 1), I'(middot) < 0.� By total differentiation� dy = c'(middot) (dy - dT) + I'(middot) dr + dG alone IS curve dG = 0, dT = 0� = > [I - c'(middot)] dy = I'(middot)dr = > dr/dy = 1 - c'(middot)/I'(middot) < 0 since c'(middot) elementof (0, 1) & I'(middot) < 0� (slope of IS curve)� the money market equilibrium condition is given by� m = L(r, y), where L_r < 0 and L_y > 0� = > by the total differentiation dm = L_r dr + L_y dy, alone the LM curve dm = 0� = > L_r dr = (-L_y)dy� = > dr/dY = -L_y/L_r > 0 since (L_4 > 0� = > (-L_4) < 0 & L_r < 0 = > ratio is positive. \r\n The goods market eq condition is given by� y = c(y - T) + I(r)