Given the following macroeconomic model of a hypothetical economy: C = 300+ + (3)(Y, -7.)- 300r, 1 = 100-100r, G = 100 L, = 0.5Y,- 200i, P=1.20 Y = C_+1+G-1 T, = -75+0.25Y, M = 7560 e) f) = 0.10 L = M/P a) Find out the initial equilibrium of the economy. b) If the central bank increases money supply once and for all to 8370, what would be its short run impact (after 5 periods) and long run impact on output and interest rate? What will be the impact of the same policy if the increase in money supply is a one-shot increase? Compare the effects of both policies on all endogenous variables. d) Using the value of truncated multiplier at the end of fourth period find the percent of total income change achieved by the end of fourth period. Also find the number of periods needed to achieve at least 80% of total income change. What factors affect the speed of realization of the variables calculated in part (d) above? Explain in detail. How would your answer to part (a) and (b) change if the money demand function were: L = 0.5Y1 - 200i, (i.e. the demand for money depends on income earned last period).