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2- The following equations describe the economy, - C = too+ on v I I= ll- l i I [i='-Ii Initially, government expenditure is $550, and taxes are $500- The real money supply equals $9. e. Derive the formulas for the IS curve and LM curve- (Jpn) b. What are the initial levels of GDP, the interest rate, eonsumption, and investment? (rm) {loving to a drop in investor I::.ondent:e1 the autonomous component of mvestmenj: drops by 90, o. By how much do income, the interest rate, and inveenrtent drop? (3pm) d.. By liov.r much should the money supply he changed in order to return GDP to its original level? What will the new interest rate had (3pm) I}. Draw three graphs to illustrate the equilibria in h, o, and d- (Spits) 3. a. Consider a causal AR(2) process Xt - $1Xt-1 - $2Xt-2 = et where et ~ WN(0, o?). Express the model as an infinite order MA process given by Xt = _jet-; and derive the difference equation for ; b. Consider the process Xt - 1.1Xt-1 + 0.3Xt-2 = et Find the first five v; values and verify your answer using ARMAtoMA function in R. c. Find the first five ACFs of the model in (b) and verify your answer using R. d. Find all PACFs of the model in (b) and verify your answer using R.intercept for the new model. S=o it becomes yr = 13in + Hi, (3) where every variable is a scalar. Suppose that (112;, air) is independent and identically distributed across 2', and {11,1- | i = 1...,N} is independent of {mi | 3' = 1 .. .,N}u1- is an error term satises that Em] : 0 and Ehrf] : I. In addition, let E[:L',;] : 1 and ELIE] = 2. While calculating the standard errors, one always needs to consider the value 2 of E [ 25:1 mini] . Please calculate its value and provide the detailed steps. (4 points)