ECON2102 - Macroeconomics 2 Assignment 1 Answer

ECON2102 - Macroeconomics 2

Assignment 1

T1 - 2020

Instructions

• Due date 7^th of March at 11.30pm. Electronic submission through Moodle. 
• Please include a complete and signed cover sheet (available on Moodle).
• This assignment is to be completed in groups of 3 or 4 students. There are no restrictions on whom you decide to form groups, i.e. your group members do not have to be from the same tutorial, presentation group and you don’t have to necessarily stick to the same group members for future group assessments. 
• You must answer all the questions, but only one of the questions will be marked. If you fail to answer one ore more questions you will be penalized.
• We advise you to firstly attempt all questions on your own then meet with your group members to discuss your individual solutions.  
• Presentation, organisation and tidiness of the assignment counts towards your mark. Make sure your solutions are clear and easy to navigate. We are looking for a simple, but well-organised general look for the assignment. 
• You are free to type or handwrite your solutions. If you prefer to type them, make sure to use Microsoft Word equations[1] (or equivalent) to write down your equations properly, otherwise reserve a space to handwrite them. If you prefer to handwrite the whole assignment or parts of it, make sure the handwriting is clear, well-organised and legible. 

QUESTION 1

This question aims to explore some of the points discussed in the first lecture, with regards to the Simple Model of Production. It is also designed to test your understanding of Chapters 3 and 4 of the prescribed textbook.

Consider an economy with the following Cobb-Douglas production function:

Further, assume the assumptions made in lecture 1 hold. Answer the following questions:

a) Provide an interpretation for the exponent of the labour input. 

b) Find expressions for the marginal product of capital (MPK) and labour (MPL) in this economy. Would you say the assumption of diminishing return to inputs is satisfied? Why? (you can add a plot if you want)

c) Derive the demand for capital from a typical firm in this economy. What can you say about the supply of capital in the simple model of production?

d) Now, suppose there is a sudden increase in the supply of capital in this economy (ie, an exogenous change in the level of capital). What do you expect to happen to the real rental rate and the real wage in this economy? Provide both mathematical and graphical explanations and economic intuition. 

QUESTION 2

This question aims to explore 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:

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: where d is a constant parameter. 

a) 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) Assuming that s = 0.4, d = 0.1, α = 0.4 and  = 1, calculate the steady state values of the variables in (a). 

Now, assume the policy-maker successfully implemented a policy that resulted in the increase of the total factor productivity level to 2 (i.e.,  = 2), ceteris paribus. 

c) 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? 

e) Is the current savings rate (s = 0.4) the golden rule of savings? Hint: you don’t need to calculate the actual golden rule, just to show that the current one is not the golden rule. 

QUESTION 3

This question aims to explore 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, as well as the effect on the plot you drew in part (d). Do you notice both a level effect and a slope effect? 

QUESTION 4

This question aims to explore some of the points addressed on our discussions surrounding unemployment issues. It is also designed to test your understanding of Chapter 7 of the prescribed textbook. 

Using the help of a diagram and clear economic explanation, discuss the effects on the equilibrium wage and employment level of an economy given the following shocks:

a) A strong increase in Australian exports, leading to a strong increase in GDP. 

b) The breakout of a new disease leads to a strong fall in consumer and business confidence, leading to a strong fall in overall production (please note this is pure fiction!). Does your answer change if wages are rigid downwards? If so, present the solution when wages are fully flexible and contrast it with the rigid case. If not, please explain in detail. 

c) The Australian government decides to increase the wage-related taxes to increase the chances of achieve a surplus in the next Budget. 

d) A natural disaster hits the Australian economy causing a large contraction on the country’s GDP, and at the same time the government announces new legislation to lower the tax rate on Superannuation contributions.