macro homework

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ECON 6620

MACROECONOMICS FOR MASTER’S STUDENTS

Fall 2020

Homework Assignment #2

Due date: Monday 5th October, 6 pm.

Instructions:

Answer ALL of the following questions.

1. Discuss the similarities and differences between the three methods in which GDP can be

measured. (10 points)

2. Answer the following three questions:

a. Derive the equilibrium level of output in the goods-market and characterize the

equilibrium graphically using the following assumptions: (6 points)

i. Consider a closed economy, so 𝑋 = 𝑀 = 0.

ii. 𝐼 and 𝐺 are exogenous or fixed variables.

iii. 𝐶 is a linear Keynesian function, so 𝐶 = 𝑐0 + 𝑐1(𝑦 − 𝑇).

iv. 𝑇 are a fixed proportion of 𝑦, so 𝑇 = 𝑡𝑦 and 𝑡 ∈ (0,1).

b. Discuss the effects of an increase in government spending on output by

considering the multiplier effect and characterize the corresponding effect

graphically. (7 points)

c. Using the assumptions in (2a) above, derive the equation for 𝑆 in equilibrium and

discuss the paradox of saving. (7 points)

3. Answer the following two questions:

a. Derive the equation for the real rate of interest 𝑟 in the economy considering that

𝑖, 𝑃 and 𝑃𝑡+1 𝐸 represent the nominal interest rate, the price level at time 𝑡 and the

expected price level at time 𝑡 + 1, respectively. (5 points)

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b. Derive the equation for the 𝐼𝑆 curve using the assumptions in (2a) above, but

consider now that 𝐼 is a linear function of 𝑟, so 𝐼 = 𝑎0 − 𝑎1𝑟. Why do we say that

𝐼 a negative function of 𝑟? What is the 𝐼𝑆 curve representing? Why is the IS curve

downward sloping? What can generate changes in the slope of the IS curve? What

can generate shifts of the IS curve? Represent the 𝐼𝑆 curve graphically. (15 points)

4. Answer the following four questions:

a. Derive the Euler equation for 𝐶𝑡 using the following assumptions: (5 points)

i. The expected present value of a household’s utility can be represented as

follows: 𝑉𝑡 𝐸 = 𝑈(𝐶𝑡 ) +

𝑈(𝐶𝑡+1 𝐸 )

1+𝜌 +

𝑈(𝐶𝑡+2 𝐸 )

(1+𝜌)2 + ⋯

ii. The functional form for the household’s utility function is constant over

time and can be represented as follows: 𝑈(𝐶𝑡 ) = log 𝐶𝑡 .

b. Considering your answer to (4a) above, discuss the implications for consumption

over time assuming that 𝜌 = 𝑟, 𝜌 > 𝑟 and 𝜌 < 𝑟. (5 points)

c. Derive the permanent income hypothesis (PIH) consumption function. Discuss the

main assumptions needed to derive the latter, and the implications for the

relationship between 𝐶 and 𝑟. (5 points)

d. Discuss the main predictions of the PIH consumption function, and the main

reasons that explain the failure of the latter. (5 points)

5. Answer the following three questions:

a. Derive the equation for the marginal 𝑞 model of investment discussing the main

assumptions needed to derive the latter. (7 points)

b. Discuss the average 𝑞 model of investment. (7 points)

c. Considering your answers to (5a) and (5b) above, discuss the type of relationship

that we expect to observe between Tobin’s 𝑞 and investment decisions. (6 points)

6. Considering your answers to (4) and (5) above, discuss how the new models for 𝐶 and

𝐼 that incorporate forward-looking behavior affect the static 𝐼𝑆 equation that you derived

in question (3b). (10 points)