please giving detailed answer thank you so much

1. Math Review: Recall the IS-LM model from your intermediate macro course. In particular, the goods-market equilibrium condition (GMEC) was Y = C (Y T )+I (r)+G, and the money-market equilibrium condition (MMEC) 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 , but less than one-for-one (i.e., 0 < C < 1). I () 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 (i.e., Lr < 0, LY > 0).

(a)(3 marks) Totally differentiate the GMEC, allowing all variables (endogenous and exogenous) to potentially vary.

(b)(3 marks) Totally differentiate the MMEC, again allowing all variables (endogenous and exogenous) to potentially vary.

(c)(3 marks) For given values of the exogenous variables, the IS curve is the combinations of Y and r that 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., find dr/dY for it). Determine the sign of this slope.1 (HINT: Which variables in the GMEC are being held constant here, and which are allowed to vary? Use this to simplify your answer from (a), and then solve it for dr/dY .)

(d)(3 marks) For given values of the exogenous variables, the LM curve is the combinations of Y and r that put the money market into equilibrium; that is, it's the solution curve for the MMEC. Find the slope of the LM curve (i.e., find dr/dY for it). Determine the sign of this slope.

(e)(6 marks) Recall that short-run equilibrium occurs when both the goods and money markets are in equilibrium, i.e., when both equilibrium conditions hold simultaneously. Let Y and r denote these short-run equilibrium quantities of Y and r. Replacing dr = dr and dY = dY in your answers to (a) and (b), solve for dr and dY explicitly in terms of dG, dT, and dm.

(f)(3 marks) Using your answers from (e), find the impact of an increase in G on the short- run equilibrium, holding the other exogenous variables constant (i.e., find dY /dG and dr/dG). Determine the signs of these derivatives.

(g)(3 marks) Using your answers from (e), find the impact of an increase in T on the short- run equilibrium, holding the other exogenous variables constant (i.e., find dY /dT and dr/dT). Determine the signs of these derivatives.

(h)(3 marks) Using your answers from (e), find the impact of an increase in m on the short- run equilibrium, holding the other exogenous variables constant (i.e., find dY /dm and dr/dm). Determine the signs of these derivatives.