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Econ 311: Advanced Macroeconomics

Problem Set 2

Due: 10 October 2023 before 11:59 PM

• Submit your assignment as a single file via CANVAS by 10 October 11:59 PM (Week 11).

• This assignment consists of 2 question sets and is worth 15% of the final grade.

• The marks allocated to the question appear next to each question.

• Use appropriate word processing software (e.g. Microsoft Word, LATEX, etc.) to write your answers.

• Use Excel/MATLAB/R/Mathematica/Python etc. to make plots and computations.

• All statements and data from external sources (other than lecture notes) needs to be properly referenced (e.g. using Harvard style).

1 Investment (9 marks)

The economy extends over time periods t = 1, 2, . . . ,∞. In each time period a unit of capital can be rented out by a representative investor to a representative firm at a price rt k . The firm uses capital to produce according to the following production function

Once the period has finished, at t + 1, the investor gets back the capital he lent out, net of depreciation, δ, and the rental income accrued.

1. Write an expression for the net present value (NPV) of the representative project of the firm. (1 mark)

2. With competitive markets, what will the rental rate on capital be? (1 mark)

3. Use your expression in (1) and rental rate in (2) to derive a condition that relates the rental rate of capital to the interest rate in the economy. Explain the forces at play that lead to this expression. (2 marks)

4. Suppose capital evolves according to the following process

Using equation (2) and your answer to (3), provide a closed-form expression for the level of investment, It , in the economy at time t. (2 marks)

5. Suppose there is an increase in the amount of labour the firm uses in production. With reference to your workings above, describe what will happen to aggregate investment and illustrate the effect with a labelled figure. (3 marks)

2 New Keynesian Model (6 marks)

Suppose a competitor to Fonterra enters the New Zealand economy and survives into the long run. What are the macroeconomic effects of this entrance and what, if any, macro-stabilisation policy do you prescribe? Use the New Keynesian framework we have developed in class to guide your answer. [You may use figures or mathematical derivations to develop your argument, but you must accompany your workings with text to explain and provide intuition for your answer.] (6 marks)