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B2. Closed Economy IS-LM-FE model: The behaviour of households and firms in a closed economy is represented by the following equations Desired consumptionC 200+0.8(Y-T-500r Desired investment : r = 200-500r Real money demand where expected inflation is ㎡-0.10 and taxes depend on income according to T 20+0.25Y. (a) Derive an expression for the IS curve with the real interest rate on the left side of the equation. How does the position of the IS curve depend on G? (b) If the money supply is M = 9890 derive an expression for the LM curve, with the real interest rate on the left side of the equation. How does the position of the LM curve depend on P? (c) If government purchases are G 196, derive an expression for the aggregate demand curve. If the full-employment output evel isY 1000, what is the price level and the real interest rate in general equilibrium? (d) Starting from the situation in part (c), suppose government purchases are increased to G 216, what are the resulting values of Y, r, P, T, Cd and Id in the short-run? (e) How does the economy adjust to its new general equilibrium after the change in part (d)? What are the resulting general equilibrium values of Y, r, P, T, Cd and 1?
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IS curve shows all combinations of income (Y) and real interest rate (r), for which the goods market is in equilibrium. LM curve shows all combinations of income and real interest rate, for which the money market is in equilibrium. Aggregate demand is the monetary value of all final goods and services produced within the boundaries of a nation. It includes consumption spending, investment spending, government spending, and net exports. The following information is given: C-200+08-)-500 I- 200-500r м -= 0.57-250(r+1) 0.10 Derive the expression for IS function as followsY=C+I+G Y = [200+0.8(T-T)-500r1+[200-500r]-G =[200+0.8(1.-20-025)-500r1+[200-500r]-G = 200 + 0.8Y-16-021-500r 200-500r G 1, 000r-G-0.41. 3 84 G-04384) 1,000 This is the function for IS curve. The position of the IS curve depends on the autonomous spending. The government spending (G) is part of the autonomous spending which does not depend on income level. Hence, an increase in G will shift the IS curve to the right and vice-versa. Suppose the money supply is 9,890. Derive the expression for LM curve as follows:9,890 0.5F-250G+7)- 0.5r-250r+0.10 0.SY-250r+25-.3 250r-0.5Y-+25 9,890 9,890 9,890 =250(0.57-9,890 This is the equation for LM curve An increase in price (P) will shift the LM curve to the left because people will need more money to pay for higher prices. The real money supply (MP) decreases leading to a higher interest rate, which lowers the demand for money Suppose the government purchases are 196. The expression for the aggregate demand is derived as followsY=C+I+G Y = [200 +0.8(Y-T)-500r]+[200-500j-G Y-[200+0.8(Y-20-025r)-500r] 1200-500r]+196 Y 200 0.8Y-16-0.2Y-500 200-500r +196 y = 580 0.61 1, 0007. 0.4Y-580-1,000r E=1,450-2.500r! This is the expression for aggregate demand. If the full employment level is Ύ-1,000, the real interest rate 1S: Y-1,450-2,500r 1,000 1,450-2,500r 2,500r 450 r 0.18 or 18% Hence, the realint is-LM) to solve for P, as follows: eres rate ism Replace the values of r and T LM equation (peneral equil brim9,890 250 9,890 0.18-50.5a.00)-30+25 39.56 0.18 2-+0.10 39.56 0.18 -2.10- 39.56 _-2.10-0.18 39.56 1.92 P 20.60 Hence, the price level is 20.60 Suppose the government purchases are increased to 216. The expression for the aggregate demand is derived as follows Y = [200+ 0.8(T-T)-500r1+ [200-500r]-G Y=[200+0.8(T-20-025Y)-500r]+[200-500r]+216 У-200+ 0.8y-16-0.27-500r + 200-500r + 216y= 600+061-1,0007. 0.41. 600-1, 000r Y = 1.500-2,500. This is the expression for aggregate demand. If the full employment level is ‘7-1 ,000, the real interest rate 1S: 1, 500-2, 500r 1,000 1,500-2,500r 2,500 500 = 0.20 or 20% Hence, the real interest rate is 20% Replace the values ofr, and y n LM equation to solve for P as25 0.20-_1 0.20-2-5956-0.10 0.20-2.10- 39.56= 1.90 P-39.56 2500.50.000)-9.890- 23 0.51,000)-+24 . .3956 1.90 P 20.82 Hence, the price level is 20.82

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