# Problem Set #4 with Answers - Economics 115 Santa Clara...

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Economics 115 Linda Kamas Santa Clara University PROBLEM SET 4 SAMPLE ANSWERS V. THE KEYNESIAN IS-LM MODEL 1. C = 150 + 0.667YD10 r (M/P)D= 0.2 Y - 10 r I = 200 - 10 r + 0.1 Y (M/P)S= 100 G = 200 NX = 50 T = 0.25 Y YD= Y - T A) (i) Derive IS Curve:ii) Derive LM Curve:C = 150 + 0.667(Y - 0.25 Y) - 10 r Money market equilibrium:(M/P)S= (M/P)DC = 150 + 0.5 Y 10 r 100 = 0.2 Y - 10 r Ep= 150+0.5Y10r+200-10r+0.1Y+200+50 Ep= 600 - 20 r + 0.6 Y solve for r: Equilibrium: Y = Ep10 r = - 100 + 0.2 Y Y = 600 - 20 r + 0.6 Y 0.4 Y = 600 - 20 r r = - 10 + 0.02 Y LM CURVEY = 2.5(600 - 20 r) Y = 1,500 - 50 r (note: it is only an accident that the solve for r: slope of the IS curve is the negative of the slope of the LM curve.) r = 30 - 0.02 Y IS CURVEiii) Equilibrium IS = LM:30 - 0.02 Y = - 10 + 0.02 Y 0.04 Y = 40 Y = 1,000Substitute Y = 1,000 into IS curve: r= 30 - 0.02 (1,000) r = 30 - 20 r = 10rYLM0IS001,0001030- 10
2(iv) C= 150 + 0.667(1,000 - 0.25x1,000) 10 (10)= 550I = 200 - 10(10) + 0.1(1,000) = 200Note: G = 200 and NX = 50 so Ep= C + I + G + NX = 550 + 200 + 200 + 50 = 1,000 = Y (v) Fiscal Surplus:BS = T G = tY G = 0.25(1,000) - 200 = 50B.If G increases to 400 (ΔG = 200) , the new planned expenditure curve is: (i)Ep= 150 + 0.5 Y 10 r + 200 - 10 r + 0.1 Y + 400+ 50 Ep= 800 - 20 r + 0.6 Y New IS curve: Y = 800 - 20 r + 0.6 Y 0.4 Y = 800 - 20 r r = 40 - 0.02 YIS shifts right/up to IS1No change in LM curve New Equilibrium:40-0.02Y =- 10+0.02Y 0.04 Y = 50 Y = 1,250r = 40 - 0.02 Y = 40 - 0.02(1,250) r = 15(iii)ΔY =1,250 - 1,000 = 250 ΔG = 400 - 200 = 200 Multiplier = ΔY/ΔG = 250/200 = 1.25The simple Keynesian multiplier (with proportional tax) = 1 = 1 = 2.0 1 - c(1-t) 1 - 0.667(1-0.25) (with a fixed tax the multiplier would be 1/(1-c) = 1/(1-.667) = 3.0)rYLM0IS001,2501530- 10IS1101,000401
3The new multiplier is smaller because the fiscal expansion raises income which raises money demand. Given money supply, this increases interest rates. Alternatively, when the Treasury sells bonds to finance the higher spending, the Treasury competes with the private sector for credit and bids up interest rates (or the excess supply of bonds will cause bond prices to fall and interest rates to rise). The higher interest ratesreduce investment and consumption, and therefore, planned expenditure falls. Thus, GDP rises less than it would have if interest rates had not risen. (iv) I= 200 - 10(15) + 0.1(1,250) = 175Investment has declined. The increase in interest rates (5 percentage points) reduced investment by 10x5 = 50, while the increase in GDP (\$250) increased investment by only 0.1x250 = 25. We cannot be certain that investment will decline. It is possible that the positive effect of GDP raising investment could be larger than the negative effect of interest rates in decreasing investment.
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