## [answered] MACROECONOMIC THEORY I ECO2142 B Fall 2016 HOMEWORK ASSIGNM

MACROECONOMIC THEORY I ECO2142 B
Fall 2016

HOMEWORK ASSIGNMENT 4 (due on December 5th)

INSTRUCTIONS: The homework is composed of two parts, questions 1-2 below, which require you to write short answers, and 5 multiple choice questions. You can upload a file with your answers to questions 1-2 in the Blackboard, or you can submit a paper copy in class or in my office. The multiple choice questions are to be answered through the Blackboard. It is your responsibility to make sure that the answers have been submitted properly.

The assignment is due by the end of the day on Dec. 5th (the deadline in the Blackboard is set at 11:59pm).

1. (50 points) In the two-period intertemporal consumption model, MRS = C2/(4C1), r = 2%, Y1 = 350 and Y2 = 153. Assume that this consumer does not have a borrowing constraint.

a. Use the MRS and the budget constraint to compute the optimal consumption combination for this consumer. Would your answer change if the consumer had a borrowing constraint? Explain your answer.

b. i. Use the optimality condition: C2/(4C1) = (1 + r) and the budget constraint to construct arelationshipbetweenC andY,Y intheform:C =? Y+ Y2 .Findthevalueofthe

parameter ?1.

ii. Find the value of ?C1 when ?Y1 = 1 and ?Y2 = 0, call this value MPCC1,Y1.Find the value of ?C1 when ?Y1 = 0 and ?Y2 = (1 + r), call this value MPCC1,Y2. Is MPCC1,Y1 = MPCC1,Y2? In other words, is the Marginal Propensity to Consume for consumption in the first period (C1) different if the change in income happens in the first period (Y1) or in the second period (Y2)? Explain your answer.

c. i. Use the optimality condition: C2/(4C1) = (1 + r) and the budget constraint to construct a relationship between C2 and Y1, Y2 in the form: C2 = ?2 [(1 + r) Y1 + Y2] . Find the value of the parameter ?2.

ii. Find the value of ?C2 when ?Y1 = 1 and ?Y2 = 0, call this value MPCC2,Y1.Find the value (1+r)

of ?C2 when ?Y1 = 0 and ?Y2 = 1, call this value MPCC2,Y2. Is MPCC2,Y1 = MPCC2,Y2? In other words, is the Marginal Propensity to Consume for consumption in the second period (C2) different if the change in income happens in the first period (Y1) or in the second period (Y2)? Explain your answer.

d. i. Use the budget constraint to construct a relationship between CT = C1 + C2 and YT = (1+r)

Y1 + Y2 in the form: CT = ?TTT. Find the value of the parameter ?T. (1+r)

ii. Find the value of ?CT when ?YT = 1, call this value M P CCT ,YT . Given your answer, what is the Marginal Propensity to Consume for total consumption (CT ) out of the total income for the two periods (YT )? Explain your answer.

2. (30 points) In this question, you will investigate the impact on consumption of an increase in the investment demand in the IS/LM model and in the two-period consumption model. Assume

1 1 2 1 1 1 (1+r)

1

that the country is a closed economy, and that the government implemented a series of incentives that increased the quantity of investment demanded at each level of the real interest rate. As a consequence, the equilibrium real interest rate in this country increased from 4% to 5%. Assume that there is no change in government spending, taxes, or monetary policy.

a. Consider the IS/LM model built from the Keynesian model.

i. Show how the change in the investment demand function will affect the IS/LM graph and the equilibrium of the model. You know that the equilibrium real interest rate will increase from 4% to 5%, but how will the equilibrium level of output change? Explain your answer.

ii. Recall that in the Keynesian model C = MPC(Y ? T). Then, how will consumption be affected by the change in the investment demand function? Explain your answer.

b. Consider now the two-period consumption model. Assume that MRS = (4C2)/C1, Y1 = 255 and Y2 = 546. Assume that this consumer does not have a borrowing constraint.

i. How will C1 and C2 be affected by the increase in the real interest rate from 4% to 5%? How will total consumption CT = C1 + C2 be affected by the change in the real interest rate? Explain your

(1+r)
answer. (Notice that when computing total consumption CT , the value of C2 discounted to the first

period will also change because of the change in r).

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