2 The equilibrium real interest rate Consider a close economy model of the short run. Assume...

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2 The equilibrium real interest rate Consider a close economy model of the short run. Assume that the government neither taxes nor spends. Private consumption and investments are given by C(t) I(t) = acY = a b (r (t) 7). You are told that output at time T is Y (T) = 70 and that the long run output is Y = 100. 1. Calculate private savings at T. 2. Calculate private investments at T. 3. Calculate the equilibrium interest rate at T. 4. For concreteness, suppose = 0.04, ac = 0.6, a1 = 0.4, and by = 30 (Note that by Y3000, so this change should not affect your numerical an- swers!) Calculate numerically consumption, investment, and real interest rate at T (Note: you must derive three real numbers. To check that you made no mistake, verify that C (T) + I (T) = 70). 5. Next, suppose that, at T + 1, the Fed reduces the interest rate to zero. How is Y (T+1) going to change in the numerical example? 6. Go to the slide titled Deriving the IS Curve." Draw the two graphs you see there for the numerical example above. The graphs must be exact, not qualitative. Show in each graph four points corresponding to r = 0, r = 0.02, r = 0.03, and r = 0.05 (you must report the corresponding four numerical values on the horizontal axis). 7. Next, we change the model and assume that some consumption behavior to take into account that some consumers are credit constrained. Specifically, C(t) = a + (Y (t) Y) == You are told, as before, that Y (T) = 70 and Y = 100. Go over questions 1-2-3 in the new setup. 8. In the case with credit-constrained consumers, for concreteness, suppose now = 0.04, ac = 0.6, = 0.5, a = 0.4, and b = 30. Calculate numerically consumption, investment, and real interest rate at T. (Note: you must derive three real numbers. To check that you made no mistake, verify that C (T) +1 (T) = 70). 9. Redo question 5 in the new model with constrained consumers. Is the reduction in the interest rate more or less effective than in the previous case in increasing demand? Provide an interpretation. 2 The equilibrium real interest rate Consider a close economy model of the short run. Assume that the government neither taxes nor spends. Private consumption and investments are given by C(t) I(t) = acY = a b (r (t) 7). You are told that output at time T is Y (T) = 70 and that the long run output is Y = 100. 1. Calculate private savings at T. 2. Calculate private investments at T. 3. Calculate the equilibrium interest rate at T. 4. For concreteness, suppose = 0.04, ac = 0.6, a1 = 0.4, and by = 30 (Note that by Y3000, so this change should not affect your numerical an- swers!) Calculate numerically consumption, investment, and real interest rate at T (Note: you must derive three real numbers. To check that you made no mistake, verify that C (T) + I (T) = 70). 5. Next, suppose that, at T + 1, the Fed reduces the interest rate to zero. How is Y (T+1) going to change in the numerical example? 6. Go to the slide titled Deriving the IS Curve." Draw the two graphs you see there for the numerical example above. The graphs must be exact, not qualitative. Show in each graph four points corresponding to r = 0, r = 0.02, r = 0.03, and r = 0.05 (you must report the corresponding four numerical values on the horizontal axis). 7. Next, we change the model and assume that some consumption behavior to take into account that some consumers are credit constrained. Specifically, C(t) = a + (Y (t) Y) == You are told, as before, that Y (T) = 70 and Y = 100. Go over questions 1-2-3 in the new setup. 8. In the case with credit-constrained consumers, for concreteness, suppose now = 0.04, ac = 0.6, = 0.5, a = 0.4, and b = 30. Calculate numerically consumption, investment, and real interest rate at T. (Note: you must derive three real numbers. To check that you made no mistake, verify that C (T) +1 (T) = 70). 9. Redo question 5 in the new model with constrained consumers. Is the reduction in the interest rate more or less effective than in the previous case in increasing demand? Provide an interpretation.