Question 1: (60 points) Consider the following numerical example of the IS-LM model in which the Central bank has an interest rate target: C = 650+ 0.18) I = 400+ 0.18 - 800i T = 500 G = 200 i = 0.1 (M/P) = 2Y - 10000i (M/P)' = 1800 a) Derive the IS and LM equations. Then, solve for the equilibrium interest rate (1), GDP (Y), investment (1) and consumption ). b) Suppose now that there is an increase in housing starts from last year to this year which increases the level of autonomous investment expenditures by $48 billion (from 400 to 448). Calculate the new equilibrium interest rate (1), GDP (Y), investment (1) and consumption (C). c) How if at all might the central bank react to the increase in housing starts to keep Y constant at the level of part a)? (i.e., suggest a policy mix). Explain in words by drawing the IS-LM diagram