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- This problem asks you to analyze the IS-LM model algebraically. Suppose consumption is a linear function of disposable income: C(YT) = a + b(YT) where a > 0 and 0 0 and d > 0. (a) Solve for Y as a function of r, the exogenous variables G and T, and the model's parameters a, b, c, and d. (b) How does the slope of the IS curve depend on the parameter d, the interest rate sensitivity of investment? Refer to your answer to part (a), and explain the intu- ition. (c) Which will cause a bigger horizontal shift in the IS curve, a $100 tax cut or a $100 increase in government spending? Refer to your answer to part (a), and explain the intuition.COURSE: MACROECONOMICS - IS-LM MODEL Demonstrate under the assumptions of the IS-LM model the effect of having a consumption function with an exogenous component, an income-dependent part and a part that depends on the interest rate. GraphConsider the following IS-LM model: C = 200 + 0.25 YD ; I = 150 + 0.25Y – 1000i ; G = 250 ;T = 200 ; (M/P)d = 2Y – 8000i ; M/P = 1600Derive the (a) IS-relation and the (b) LM-relation.Solve for the equilibrium (c) real output and (d) interest rate.(e) Solve for the equilibrium values of C and I and verify yourequilibrium output by: Y = C + I + G(f) Now suppose that the money supply increases to M/P = 1840. Solve for Y, i, C, I and describe in words the effectsof monetary expansion.(g) Set M/P to its initial value 1600. Suppose, that governmentspending increases to G=400. Summarize the effects offiscal expansion on Y, i, and C.
- Consider an economy that begins in a situation in which output equals potential output. Consider the modified representation of the IS-LM diagram in which the y-axis is the nominal interest rate versus the real interest rate, where we take into account the presence of the zero lower bound (Graph A). Suppose that a collapse in house prices impacts the economy. 1. Use either the 4-point curved line drawing tool or the line drawing tool to show the effect on either the IS or the LM curve. Hint: Only one curve will shift. 2. Use the point drawing tool to indicate the new equilibrium output and nominal interest rate. Carefully follow the instructions above and only draw the required objects. Graph A 0- урот e₁ LM IS Select Line 4-point Curve PointThe consumption function is given by: C = 200+0.75 (Y-T). The investment function is I = 200-25r. G =100 T=100 Suppose instead that money supply is raised from 1,000 to 1,200. How much does the LM curve shift? What are the new equilibrium interest rate and level of income?Q15 Which of the following statements is consistent with a given (i.e., fixed) LM curve? Select one: a. A reduction in the interest rate causes money demand to decrease. b. A reduction in the interest rate causes investment spending to increase. c. An increase in output causes an increase in demand for goods d. An increase in output causes an increase in money demand.
- 3-) Consider an economy with the following economic functions; cd=1000+ 0.45Y - 45000r - 0.5G Id = 500 22500r Md -0.5Y - 3000 P And other variables are ² = 0.04, G=250, Y = 500, and M = 4200. a) Find the equilibrium values of the real interest rate, consumption, investment, and the price level. b) Suppose the money supply increases to 8400. Find the equilibrium values of the real interest rate, consumption, investment, and the price level. (Assume that the expected inflation rate is unchanged)What is the impact of monetary and fiscal policy if (a) money demand does not depend on income, LM curve is horizontal; and (b) If money demand is extremely sensitive to interest rate, LM curve is horizontal.a) consider the following IS–LM model: C = c1(Y - T) I = b1Y - b2i M/P = d1Y - d2i Solve for equilibrium output. Assume c1 + b1 < 1. b) Solve for the equilibrium interest rate. (Hint: Use the LM relation.) c) Solve for investment.
- Assume that the long-run level of output is Y = 1000, which the economy is also at initially in the short-run. Suppose that the consumption and investment functions are, respectivley, C = 100 + 0.8(Y –- T), I = 100 – 2000r, %3D that is, MPC is 0.8. Furthermore, the LM (money market equilibrium) curve is 200i The government is currently implementing a policy Ğ = 80, T = 50, %3D and the central bank (CB) is supplying M = 1000. Expected inflation is aº = 0. Suppose that pre-Covid, short-run output was equal to long-run output at Y = 1000. Fill in the following table that describes this short-run equilibrium. That is, solve for the values of the nominal interest rate, short-run price level, consumption, and investment. I' %An economy is described by the following equations: C = 2,600+ 0.8 (Y- T) - 10,000r IP = 2,000 10,000r G = 1,800 NX = 0 T = 3,000 The real interest rate, expressed as a decimal, is 0.10 (that is, 10 percent). a. Find a numerical equation relating planned aggregate expenditure to output. Instructions: Enter your response for mpc rounded to one decimal place. PAE=+ 0.8 Y b. Using a table (or algebra if you have used the appendix to this chapter), solve for short-run equilibrium output. Instructions: If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Leave no cells blank. You must enter 'zero' for the answer to grade correctly. Output Y 9,500 9,600 9,700 9,800 9,900 10,000 10,100 10,200 Planned aggregate expenditure (PAE) Short-run equilibrium output: Y PAEAn IS curve shows: (a) that realized savings are most likely a function of interest rates, because changes in interest rates result in changes in precautionary demand for money; (b) the combinations of investments and incomes that result in the supply and demand for money being equal to one another; (c) the locus of all combinations of interest rates and incomes that will result in realized investment and realized savings being equal to one another; (d) that increases in output typically are caused by increases in interest rates.