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ECON 304 - PRACTICE PROBLEM #1 FOR FINAL EXAM - SAMPLE 'BIG PROBLEM' - SIMILAR TO WHAT YOU WILL SEE ON FINAL EXAM: IS : MP: Y = 16 - r r = r(bar) + λ π SRAS: π= π -1 + 1 ( Y - Y P) + p Potential GDP: YP = 17, π -1 = 1.5%, λ = .5, r(bar) = 0, p =0 a) (10 points) Derive an expression for the IS curve....Y in terms of r Y = [ 3 + 2.2 -.2 + 3.0 + 1.5 - 1.5] x (1 / 1 - .5) - (.1 + .2 + .2)/(1 - .5) r Y = 16 - r b) (5 points) Derive an expression for Aggregate Demand AD: Y = 16 - [ 0 + .5 π)........AD: Y= 16 - .5π 1 c) (5 points) Find the value of GDP Y= 16 - .5 [1.5 + 1( Y - 17) + 0] Y(1 + .5) = 16 - .75 + 8.5 Y = 23.75 / (1 + .5)......Y = 15.833 d) What is the GDP gap? (15.833 - 17) / 17 = - 6.86% e) Find the values of π and r π = 1.5% + 1(15.833 - 17) + 0] ......= .333% = π r = 0 + .5(.333) .......r = .167% DRAW FOUR DIAGRAMS - AN MP CURVE DIAGRAM TOP LEFT, AN 'IS' CURVE DIAGRAM ON TOP RIGHT, AND A AS/AD DIAGRAM BELOW THE 'IS' CURVE AND A PHILLIPS CURVE DIAGRAM ON THE BOTTOM LEFT. PLEASE BE SURE TO COMPLETELY LABEL DIAGRAMS LABEL THESE INITIAL CONDITIONS AS POINT A ON ALL FOUR DIAGRAMS. f) If the Fed wanted to eliminate the GDP gap, what would they need to do exactly? Assume inflation expectations stay at 1.5%. Show this as points B on all four diagrams. need to get inflation to = 1.5% (SRAS) and r = -1% (IS) -1 = r bar + .5 (1.5) ..... r bar = -1.75%....so the Fed would need to lower rbar from 0 to -1.75% g) What is the new expression for the AD curve AD: Y = 16 - [ -1.75 + .5 π)........AD: Y= 17.75 - .5π h) Suppose that the Fed did not do anything and were counting on expansionary fiscal policy - suppose the Government increases spending (infrastructure) by $ 1 Trillion. What is the new expression for the IS curve now? Y = [ 3 + 2.2 -.2 + 4.0 + 1.5 - 1.5] x (1 / 1 - .5) - (.1 + .2 + .2)/(1 - .5) r Y = 18 - r i) Resolve for the new Y, π and r. Again, assume that inflation expectations are unchanged. Label as points C on your four diagrams. Y= 18 - .5 [1.5 + 1( Y - 17) + 0] Y(1 + .5) = 18 - .75 + 8.5 Y = 25.75 / (1 + .5)......Y = 17.166 π = 1.5% + 1(17.166 - 17) + 0 ......= 1.66% = π r = 0 + .5(1.66) .......r = .83% 2 j) Let's go back to the original conditions at points A. Assume that the Fed does not change policy and that there is no change in fiscal policy either. According to the self correcting mechanism, how will the economy return to full employment - explain how this self correcting would work and explain, don't show, how each diagram would be effected. Are you confident that this self correcting mechanism would work, why or why not? Draw points A and B and C in S = I closed economy diagram (ignore net exports) - be sure to label relevant shift variables. Now draw points A, B , and C in an MPK / uc diagram Recall Homer (the borrower) and Dagwood (the saver) - which do each consumer prefer? A move from A to B or a move from B to C? Explain. 3