Which of the following two statements involves positive economic analysis and which
Economics 1 — Semester 2 — Tutorial Sheet 9 — Week 10
The Interest Rate and Production in
the Short Run
Required reading
- Recent lecture notes
- Nils Gottfries, Macroeconomics, Chapter 8
(Note: it is assumed here and will be assumed in the exam that you are familiar with the
terminology laid out on pages xxvi - xxvii of Gottfries’ text.)
Homework
- Submission of homework this semester works like semester 1, but there is now
one additional component – you must also submit a graph.
- The submission must be done via Learn by 5pm on the Sunday before the tutorials
occur.
- The written homework, as before, should be equivalent to at least two sides of
handwritten A4 and should be clear enough to read. Again, it does not need to be
complete, and indeed it does not even need to be co
ect. You just need to show
that you have made an honest attempt. As long as you have shown an honest
attempt, you will get credit, and as long as you do this for 14 of the 18 tutorials
during the year, you will get full credit.
- NEW FOR SEMESTER 2: you must also submit an additional page with a ‘looking
at the data’ graph (this will be different each week, and relevant information will
e on each tutorial sheet).
Further resources
- Gottfries on YouTube: the textbook author (Nils Gottfries) has put 15-40 minute
videos from most chapters of the book on YouTube:
o https:
goo.gl/Wq8o82
- FRED: Most of the tutorial sheets this semester contain graphs generated by the
St. Louis Fed’s Federal Reserve Economic Data (FRED) site. This is a surprisingly
easy-to-use, free site for exploring hundreds of thousands of economic data series.
You are strongly encouraged to visit the site whenever you feel the need to find
out what’s happened lately to GDP growth, or inflation, or infant mortality, etc.
o http:
esearch.stlouisfed.org/fred2
Recordings:
- Questions marked with an asterisk* have video solutions recorded by Sean, which
will be released after the Sunday 5pm submission deadline. Because the asterisk
questions are covered in video, they will mostly not be covered within the
tutorials themselves.
Note
- This is the final tutorial of the year, but there will be a supplemental question sheet about
Chapter 9 posted on Learn, and the material in the supplemental sheet is examinable in the
final exam.
https:
goo.gl/Wq8o82
http:
esearch.stlouisfed.org/fred2
Looking at the data
Using FRED (or another data source) find and print a graph of investment and the nominal
interest rate for a country of your choice. Include comments on any trends or features in
the data and
ing the printed graph and comments to your tutorial.
Tutorial Questions
Q1. Targeting interest rates. We have the following model:
(1) ? = ? + ? production = demand
(2) ? = ?? + ?? consumption function
(3) ? = ?? − ?? investment function (?? > ? & ? > ?)
(4) ? ?⁄ = ?? − ?? money market equili
ium (? > ? & ? > ?)
(a) Illustrate the consumption function in a diagram with production on the horizontal
axis and consumption on the vertical axis. Interpret the parameters ?? and ?.
(b) Illustrate the investment function in a diagram with the interest rate on the vertical
axis and investment on the horizontal axis. Interpret the parameters ?? and ?.
(c) Suppose that the central bank holds the interest rate constant. Use equations (1) -
(3) to solve for production for a given interest rate. Illustrate this relation in a
diagram with production on the horizontal axis and the interest rate on the vertical
axis. What is the name of this relation?
(d) Use the result in (c) to calculate the effect on production of an increased willingness
to invest, represented by ??? > ?.
(e) Use the result in (c) to calculate the effect of an increase in the interest rate on
production and interpret the result. How does the effect depend on the parameters
d and b? Explain.
(f) What is the role of equation (4) when the central bank sets the interest rate at some
target level?
Q2. Targeting the money supply. Use the same model as in the previous exercise but now
assume that the central bank keeps the money supply constant. Then the endogenous
variables are Y, C, I, and i.
(a) Rewrite equation (4) with the interest rate on the left-hand side. How does the
interest rate depend on production according to equation (4)? Illustrate this
elation in a diagram with production on the horizontal axis and the interest rate
on the vertical axis. What is the name of this relation?
(b) Use the result in a) to substitute for the interest rate in the investment function.
Then use the result and (2) to substitute for I and C in equation (1) and solve for
production for a given money supply.
(c) Use the result to calculate the effect of an increased willingness to invest
epresented by ??? > ?.
(d) Compare the result to the earlier exercise when the central bank keeps the interest
ate constant. In which case do we get the biggest effect on production? Why?
Illustrate the difference using the IS and LM curves.
(e) How do the parameters e and f affect the result above? Explain.
Q3. The slope of the IS curve. Consider the following model of aggregate demand:
? = ? + ?
? = ? + ?? + ???
? = ? − ?(? − ??)
(a) Give economic interpretations to the equations and the coefficients a, b, c, d and f.
(b) Substitute the second and third equation into the first and solve for Y.
(c) Calculate the effect of an increase in expected future income, ??, on aggregate
demand and production. Explain the result.
(d) Calculate the effect of an increase in the interest rate, i, on aggregate demand and
production. Explain the result.
(e) What is the slope of the IS curve for this economy?
(f) How do b and f affect the slope of the IS curve? Explain.
Q4. Increasing the money supply. Consider the money market equili
ium condition:
?
?
=
?
?(?)
For some time, the money supply, M, is constant and then there is a one-time increase in the
money supply. How does this affect production, Y, the price level, P, and the interest rate, i…
(a) …in the short run?
(b) …in the long run?
Q5. Getting to equili
ium in IS-LM.
(a) Consider point A in the figure above. Is this an equili
ium point? Why/why not?
What would you expect to happen if the economy was initially at point A?
(b) Do the same analysis for point B.
i
LM
IS
Y
B i2
i1
Y1
A
Q6. Introducing government. We now introduce taxes and government demand for goods
and services. We assume that the tax increases with income. We assume that the central
ank holds the interest rate constant.
(1) ? = ? + ? + ? production = demand
(2) ? = ?? + ?(? − ?) consumption function (? < ? < ?)
(3) ? = −?? + ?? tax schedule (? < ? < ?)
(4) ? = ?? − ?? XXXXXXXXXXinvestment function (?? > ? & ? > ?)
(a) Use the equations to find the level of production for a given interest rate.
(b) Assume that the government starts to demand more goods and services so that ??
?. Use the result in (a) to calculate the effect on production. How does the effect
depend on the marginal tax? Explain.
(c) Suppose that the government reduces taxes by increasing ??. What happens to the
tax schedule? Use the result in (a) to calculate the effect on production. How does
the effect depend on the marginal tax? Explain.
* Q7. India’s 2016 cu
ency reforms. Please read the (short!) Economist article on India’s
2016 cu
ency reforms included with this week’s material1.
(a) What was the stated purpose of the 2016 reforms? What did the government
actually do?
(b) Did the reforms have their intended effect?
(c) What was the initial effect of the reforms on the price level and output?
(d) How would you model the reforms in terms of the IS-LM model? Are the IS-LM
predictions in line with the results discussed in part (c)?
* Q8. Liquidity constraints and permanent income. Suppose that labour income increases by
100 million. Among the consumers, 20% have no assets and just consume their cu
ent
labour income. The other 80% behave in accordance with the consumption theory
presented in Chapter 4. Of the increase in income, 50% is perceived as permanent increase
in real income and 50% as a temporary increase which will be reversed next year. Make a
ough calculation of the effect on consumption (and thus the marginal propensity to
consume).
Q9. Technological progress and the IS curve. Suppose that production is initially at the
natural level, then a new technology is discovered, which makes it possible to produce much
more fuel-efficient engines for cars.
(a) How will this affect investment, consumption, and the IS curve? (Hint: how are the
variables in the investment and consumption functions affected?)
(b) What happens to production and the interest rate if the central bank keeps the
money