(Solved): 3. Consider the IS-LM model characterized by the following equations: \[ \begin{array}{l} C=300+.5 ...

3. Consider the IS-LM model characterized by the following equations: \[ \begin{array}{l} C=300+.5(Y-T) \\ I=100+.25 Y-800 i \\ G=200 \\ T=40 \end{array} \] a) Write the expression for \( \mathrm{Z}(\mathrm{Y}, \mathrm{i}) \) b) Derive the IS curve, Y(i) c) Discuss the relationship between output and the interest rate along the IS curve and the intuition behind it. d) What is the equilibrium level of output if \( \bar{\imath}=.05 \) ? e) Suppose real money demand is described by \( \frac{M}{P}=Y-1000 i \). What is the level of real money supply when the IS-LM model is in equilibrium? f) Solve for \( \mathrm{C} \) and \( \mathrm{I} \) in equilibrium. g) Verify those are the correct equilibrium values by adding up \( \mathrm{C}+\mathrm{I}+\mathrm{G} \) h) Suppose the central bank cuts to interest rate to \( 3 \% \). How would this change the LM curve? i) Solve for the new equilibrium values of Y, I, C, and real money supply. j) Draw the monetary policy expansion on the IS-LM diagram and describe the effect of the policy in words.