ECOS3010: Assignment 1 (Total: 20 marks) Due 11:59 pm, Friday Apr 4, 2025
1. This work must be turned in by the deadline. Work not submitted on or before the due date is subject to a penalty of 5% per calendar day late. If work is submitted more than 10 days after the due date, or is submitted after the return date, the mark will be zero. Each assignment is worth 10% of total weight.
2. TYPE your work (including all mathematical equations). Homework must be submitted as a typed PDF file, with no exceptions. Untyped work will not be graded and will receive a mark of zero. If any question requests a graph, you may draw the graph by hand, scan it, and include it as a figure in the PDF. Please do not forget to include your name and SID.
3. As you answer the questions, you need to clearly demonstrate your understanding of economics and relevant methodology through your working process. Detailed and logical presentation of the process is crucial and helpful for solving the problem and earning higher grades.
PROBLEM 1. (10 Marks) In our study of a simple model of money, we rep- resented economic growth through a growing population. Taking into account the money market clearing condition, consider the population growth is given as follows:
Nt+1 = nNt
Each young person born in period t is endowed with yt units of the consumption good when young and nothing when old. The endowment grows over time so that:
yt+1 = αyt
where α > 1. Assume that in each period t, people desire to hold real money balances equal to θ of their endowment, where 0 < θ < 1 so that:
vtmt = θyt
Consider there is constant stock of fiat. money, M .
(a) Derive the lifetime budget constraint. [2 marks]
(b) What is the condition that represents the clearing of the money market in an arbitrary period t? Determine the real return of fiat money in a monetary equilibrium. How does the percentage of holding endowment affect t he r eal r eturn o f fi at money? [2 marks]
(c) Using the database developed by the World Bank (World Development Indi- cators Link), find the data for Malaysia from 2000 to 2023 to determine the values for α and n. Assess whether the value of money in Japan is increasing or decreasing. Briefly Discuss the implications for the price level. [Hint: For simplicity, use the arithmetic mean for GDP growth (annual %) and population growth (annual %), and round the final result to four decimal points.] [4 marks]
(d) Now relax the assumption of constant stock of fiat money, which implies:
Mt+1 = zMt
Derive the new rate of return on fiat money for Japan over the selected period.
Do you obtain a different result for the value of money in Malaysia and its implications for the price level? [Hint: For simplicity, use the arithmetic mean for broad money growth (annual %), and round the final result to four decimal points.] [2 marks]
PROBLEM 2. (10 Marks) Let us extend our model from two periods to a four-period economy. Agents are endowed with y0 when they are young. In their youth, they do not work as they are accumulating skills for the next period. During the second period and third period, agents enter the l abour force and receives wage compensation, which equals to ω2 and ω3, respectively. In the fourth and final period, agents retire and enjoy all the money holdings accumulated from the previous periods. The real interest rate is r. Agent discounts future utility at rate β. The agent's lifetime utility function is given as:
where utility function for consumption and labour are
We use a simple notation of real demand for fiat money (money holdings) from textbook, where qt = vtmt. All parameters are assumed to be positive. For your understanding, the first-period budget constraint is given as:
The second-period budget constraint is:
The third-period budget constraint is:
The fourth-period budget constraint is:
and,
As the central planner, you are concerned about consumption decision for agents and thinking about the labour supply of the agents.
(a) Derive the lifetime budget constraint. [1 mark]
(b) Setup the Lagrangian equation to represent the optimisation problem. [1 mark]
(c) Derive the optimum consumption levels in each period. [4 marks]
(d) Derive the optimal labour function. [2 marks]
(e) How does the initial endowment y0 affect the agentIs labour supply? Explain the economic intuition behind this result? [2 marks]