ECON2102 - Macroeconomics
2 Assignment 1
Name:___________________
zID:_____________________
Instructions
- Due date 3th of October at 5:30pm. Electronic submission through Moodle in the Assignment
section and use the Submission link associated with the Tutorial Day and Time that you are
registered in.
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- This assignment is graded over 50 marks, but worth 10% of the final grade.
- This assignment is to be completed individually.
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1
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QUESTION 1 (25 marks)
This question explores some of the points discussed in Topic 2 (Solow-Swan model). It is also designed to
test your understanding of Chapter 5 of the prescribed textbook.
Consider an economy with the general Cobb-Douglas production function: = 1−.
Answer the following questions assuming that labour grows at the rate n = 0 and adopting the assumptions
made in lecture. The equation describing capital dynamics is: +1 = + −
where d is a constant parameter.
a) (9 narks) Obtain the steady state levels of the capital stock (K), output (Y), capital per worker (k), output
per worker (y), consumption per worker (C/L), total savings (S), private investment (I), real wages (w) and
real interest rates (r). Make sure to show all your work.
b) (8 marks) Assuming that s = 0.4, d = 0.1, α = 0.2, ̅ = 1 and ̅ = 1, calculate the steady state values of the
variables in (a).
Now, assume the policy-maker successfully implemented policies that resulted in the increase of the total
factor productivity level to 2 (i.e., ̅ = 2), ceteris paribus.
c) (8 Marks) Using the help of the Solow-Swan diagram developed in lectures and tutorials, explain the
effect of this policy on the standard of living of the economy. Make sure to include:
i) The economic explanation of why the economy experienced a change in the steady state level of
capital per worker;
ii) A diagram illustrating what happened to the relevant curves.
iii) Another diagram illustrating the dynamics of the stock of capital in the economy (before, at and
after the technological shock).
iv) What must have happened to the growth rate of output per worker in the transition between the
initial equilibrium and the final one?
QUESTION 2 (25 marks, 5 marks each question)
This question explores some of the points discussed in Topic 3 (Romer model). It is also designed to test
your understanding of Chapter 6 of the prescribed textbook.
Consider the simple Romer model developed in lectures with the following values for parameters:
a) How fast are ideas growing in this economy in percentage terms? How many workers are being employed
in the goods sector?
b) Find what the stock of ideas in this economy will be in periods 200 (t = 200) and 400 (t = 400).
c) Find an expression for the output per worker in the balanced growth path. What will be the standard of
living in periods 200 and 400?
d) On a clear graph, plot the trajectory of the log of output per worker through time.
e) Now, assume the policy-maker decides to allow 100 extra workers to come from overseas, leading to an
increase in the total labour force to 1,000. Show the effects of this change on the growth rate of ideas.