ECON 2123 Macroeconomics, Spring 2019
Instructor: Prof. Wenwen Zhang
Problem Set 1
Name:_________________________________________
Student ID: ______________________
Important Notes:
• Please print this Problem Set out (A4 size, single-sided or double-sided, one page on one side)
and write down your answer in the spaces provided.
• You should submit a hard-copy of your solution to the Homework Submission box on 6/F of LSK
near Lift 3-4.
• This problem set is due on 12 March 2019 at 6pm. No late submission will be accepted.
Problem 1
Suppose that an economy shows only the following activities in a specific year:
i.
ii.
It costs an automobile manufacturing company $7 million to assemble 4,000 cars. The
cars are then sold to stores for $10 million.
The stores pay their workers an annual wage of $2.5 million, and then sell the cars
directly to the consumers for $18 million.
a) Calculate the GDP in this economy using the production-of-final-goods approach.
b) Calculate the GDP using the value-added approach. Show the value added at each stage of
production.
c) Calculate the GDP using the income approach. Show the costs incurred and profit earned.
1
Problem 2
An economy produces three goods: computers, phones, and apples. Quantities and prices per unit for
year 2016 and 2017 are as followings:
2016
2017
Quantity
Price (¥)
Quantity
Price (¥)
Computers
20
2000
24
3000
Phones
8
1000
12
500
Apples
2000
1
2000
10
a) What is nominal GDP in 2016 and in 2017? By what percentage does nominal GDP change from
2016 to 2017?
b) Using the prices for 2016 as the set of common prices, what is real GDP in 2016 and in 2017? By
what percentage does real GDP change from 2016 to 2017?
c) Using the prices for 2017 as the set of common prices, what is real GDP in 2016 and in 2017? By
what percentage does real GDP change from 2016 to 2017? Why are the two rates different from
answers in (b)? Which one is correct? Explain briefly.
d) Using the prices for 2016 as the set of common prices. Compute the GDP deflator for 2016 and for
2017, and compute the rate of inflation from 2016 to 2017.
e) Using the prices for 2017 as the set of common prices. Compute the GDP deflator for 2016 and for
2017, and compute the rate of inflation from 2016 to 2017. Why are the two rates different from
answers in (d)? Which one is correct? Explain briefly.
2
Problem 3
The following equations refer to the goods market of an economy in billions of dollars:
𝐶 = 360 + 0.25𝑌𝐷
𝐼 = 125; 𝑇 = 80; 𝐺 = 250
a) Solve for the goods market equilibrium output.
b) Find the equilibrium disposable income. Hence, find equilibrium consumption.
c) Calculate the public savings. Hence, calculate the private saving without using equilibrium output.
d) Calculate the multiplier. Explain how it affects equilibrium output.
e) Suppose that the government decides to increase its spending from $250b to $500b.
Find the equilibrium output, consumption, and disposable income. Give one reason of why the
government would expand fiscal spending during economic recession.
3
Problem 4
Automatic stabilizers
In this chapter we have assumed that the fiscal policy variables G and T are independent of the level of
income. In the real world, however, this is not the case. Taxes typically depend on the level of income,
and so tends to be higher when income is higher. In this problem, we examine how this automatic
response of taxes can help reduce the impact of changes in autonomous spending on output.
Consider the following behavioural equations:
𝐶 = 𝑐0 + 𝑐1 𝑌𝐷
𝑇 = 𝑏0 + 𝑏1 𝑌
𝑌𝐷 = 𝑌 − 𝑇
𝑐0 , 𝑏0 , G, and I are positive constant. Assume that 0 < 𝑏1 < 1.
a) Solve for the equilibrium output, and equilibrium consumption.
b) What is the multiplier? If 𝑏1 decrease, does the economy respond more to changes in autonomous
spending?
c) With reference to the multiplier presented in Chapter 3, how this automatic response of taxes can
help reduce the impact of changes in autonomous spending on output
(cont’d, Problem 4)
Balanced budget versus automatic stabilizers
It is often argued that a balanced budget amendment would be destabilizing.
d) Solve for taxes in equilibrium.
4
Suppose that the government started with a balanced budget, and there is a drop in I.
e) What happens to output? What happens to taxes? What happens to the fiscal balance?
f)
Suppose that after the decrease in investment, the government wishes to keep the budget
balanced. What will be the effect on output? Does this fiscal policy counteract or reinforce the effect
of the drop in I on output?
Problem 5
Suppose that the household nominal income for an economy is $60 trillion, and the demand for money
in this economy is given by
𝑀𝑑 = $𝑌(0.1 − 0.4𝑖)
a) What is the demand for money when the interest rate is 1% and 5%?
b) What will be the impact on the demand for money if the nominal income declines by 10%?
c) What is the relationship between the demand for money and income? Money demand and the
interest rate?
d) Explain what the central bank should do to interest rates if it needs to decrease the demand for
money.
5
Problem 6
Suppose that a person’s wealth is $55,000 and that her yearly income is $40,000. Also suppose that her
money demand function is given by
𝑀𝑑 = $𝑌(0.5 − 𝑖)
a) Derive the demand for bonds. Suppose the interest rate increase by 5 percentage points. What is
the effect on her demand for bonds?
b) What are the effects of a decrease in wealth on her demand for money and her demand for bonds?
c) What are the effects of a decrease in income on her demand for money and her demand for bonds?
Problem 7
Consider the goods market model with endogenous investment, where I is depend on both sales and the
interest rate:
𝐼 = 𝑏0 + 𝑏1 𝑌 − 𝑏2 𝑖.
a) Solve for equilibrium output. At a given interest rate, is the effect of a change in autonomous
spending bigger than if investment was exogenous? Why? (assume 𝑐1 + 𝑏1 < 1. )
6
The LM relation is
𝑀
𝑃
= 𝑑1 (𝑌 − 𝑑2 𝑖).
b) Solve the IS-LM equilibrium output. Derive the multiplier (the effect of a change of one unit in
autonomous spending on output).
c) Is the multiplier you obtained in part (b) larger or smaller than the multiplier in exogenous
investment goods market model? Explain how your answer depends on the parameters in the
behavioural equations for consumption, investment, and money demand.
7
Problem 8
Consider the following IS_LM model:
1
𝐶 = 200 + 𝑌𝐷
3
1
𝐼 = 150 + 𝑌 − 1000𝑖
3
𝑀 𝑑
( ) = 2𝑌 − 8000𝑖
𝑃
𝐺 = 250; 𝑇 = 200;
a) Derive the IS relation. (Hint: Y as the subject)
b) Derive the LM relation. (Hint: 𝑖 as the subject)
c) Solve for the equilibrium interest rate and output.
8
𝑀
= 1600
𝑃
d) Solve for the equilibrium consumption and investment. Verify that the value you obtained for 𝑌 by
𝐶+𝐼+𝐺
e) Now suppose that the money supply increases to
𝑀
𝑃
= 1840. Solve for 𝑌, 𝑖, 𝐶, and 𝐼. Describe in
words, the effects of an expansionary monetary policy.
f)
Now suppose that the money supply decreases back to
𝑀
𝑃
= 1600. Instead, government spending
increases to 𝐺 = 400. Solve for 𝑌, 𝑖, 𝐶, and 𝐼. Describe in words, the effects of an expansionary fiscal
policy.
(end of Problem Set 1)
9