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

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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 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, M RS = 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

b. i. Use the optimality condition: C2 /(4C1 ) = (1 + r) andh the budget

i constraint to construct

Y2

a relationship between C1 and Y1 , Y2 in the form: C1 = ?1 Y1 + (1+r) . Find the value of the

parameter ?1 .

ii. Find the value of ?C1 when ?Y1 = 1 and ?Y2 = 0, call this value M P CC1 ,Y1 .Find the value of

?C1 when ?Y1 = 0 and ?Y2 = (1 + r), call this value M P CC1 ,Y2 . Is M P CC1 ,Y1 = M P CC1 ,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

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 .

1

ii. Find the value of ?C2 when ?Y1 = (1+r)

and ?Y2 = 0, call this value M P CC2 ,Y1 .Find the value

of ?C2 when ?Y1 = 0 and ?Y2 = 1, call this value M P CC2 ,Y2 . Is M P CC2 ,Y1 = M P CC2 ,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

C2

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

and YT =

Y2

Y1 + (1+r)

in the form: CT = ?T TT . Find the value of the parameter ?T .

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 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 = M P C(Y ? T ). Then, how will consumption be affected

b. Consider now the two-period consumption model. Assume that M RS = (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

C2

total consumption CT = C1 + (1+r)

be affected by the change in the real interest rate? Explain your

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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