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)S = 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 a decrease in consumer confidence from last year to this year which decreases the level of autonomous consumption expenditures by $96 billion (from 650 to 554). Calculate the new equilibrium interest rate (1), GDP (Y), investment (I) and consumption c) How if at all might the central bank react to the decrease in consumer confidence 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