Assignment 1 (Total: 50 marks) Due 11:59 pm, Friday, September16, 20221. Homework must be turned in on the day it is due. Work not submitted on or beforethe due date is subject to a penalty of 5% per calendar day late. If work is submitted morethan 10 days after the due date, or is submitted after the return date, the mark will bezero. Each assignment is worth 10% of total weight.2. TYPE your work (including all mathematical equations). Homework issubmitted as a typed .pdf file, no exceptions. Untyped work will not be marked and willreceive a mark of zero. You can draw a graph by hand, scan it, and include it as a figure inthe PDF. Please don’t forget to include your name and student number.3. Carefully explain your work.Question 1-5. Answer True, False or Uncertain. Briefly explain your answer. (eachquestion 4 marks)1. The lack of double coincidence of wants precludes people from using credit for trans-actions.2. Consider stationary allocations in the OLG model of money. Individuals consumethe same amount of good when young and when old.3. The optimal monetary policy in the OLG model of money is to have deflation.4. In the Lucas price surprise model, a higher growth rate of money supply leads to alower level of output under nonrandom monetary policy.5. The Lucas critique indicates that the government can use a random monetary policyto stimulate output.6. (10 marks) Consider the standard OLG model with money. Individuals are endowedwith y units of a perishable consumption good when young and nothing when old. Thereare N individuals in every generation. Each generation has identical preferences whereu (c1,t, c2,t+1) = c1/21,t + c1/22,t+1. There exists one asset in the economy – money. The moneysupply grows at a constant rate z, whereMt = zMt?1 and z > 1. The new money created isused to finance government purchases of g goods per young individual in every period. Theinitial old are endowed with M0 units of money. In the following, we focus on stationaryallocations.(a) Find an individual’s budget constraints when young and when old. Combine themto form the individual’s lifetime budget constraint. (2 marks)(b) Solve for the optimal consumption allocation (c?1, c?2) chosen by the individual in astationary monetary equilibrium. How do (c?1, c?2) depend on z? (2 marks)(c) Find the government budget constraint. Express government purchases g as a func-tion of z and other parameters in the model. (2 marks)Now instead of being endowed with y units of the consumption good, individuals cansupply labour ?1,t only when young. That is, the young supply labour ?1,t and consume c1,t,but the old can only consume c2,t+1. One unit of labour supply produces one unit of theconsumption good. Each generation has identical preferences whereu (c1,t, c2,t+1, ?1,t) = c1/21,t + c1/22,t+1 ? ?1,t.(d) Find an individual’s budget constraints when young and when old. Combine themto form the individual’s lifetime budget constraint. (1 mark)1(e) Solve for the optimal consumption and labour supply (c?1, c?2, ??1) chosen by the indi-vidual in a stationary monetary equilibrium. (2 marks)(f) How do (c?1, c?2) depend on z? How does ??1 depend on z? Briefly explain the intuitionfor your answer. (1 mark)7. (10 marks) Consider the OLG model that we develop in class. There are N people inevery generation. Each individual is endowed with y units of goods when young and nothingwhen old. Suppose that monetary authority prints fiat money at the rate z but now doesnot distribute the newly printed money as a lump-sum transfer to the old. Instead, thegovernment distributes the newly printed money by giving each old individual new dollarsfor each dollar acquired when young.(a) Use the government budget constraint to find α as a function of z. (2 marks)(b) Write down the individual’s budget constraints when young and old. Combine themto form the individual’s lifetime budget constraint. (2 marks)(c) What is the inflation rate pt+1/pt? What is the real rate of return on fiat money?(2 marks)(d) Graph the stationary monetary equilibrium. Carefully label the axes and the optimalallocation. (1 mark)(e) Write down the resource constraint faced by a planner. (1 marks)(f) Compare the individual’s lifetime budget constraint with the resource constraint.Demonstrate that the monetary equilibrium satisfies the golden rule allocation regardlessof the rate of inflation. Explain why inflation does not induce individuals to reduce theirreal balances of money in this case. (2 marks)8. (10 marks) Figure 7.1 and Figure 7.2 in Chapter 7 show the correlation between in-flation and unemployment in the US in different periods of time. Using the OECD database(https://data.oecd.org/), find quarterly data on the inflation rate (CPI based) and the un-employment rate for Australia. Plot the correlation between inflation and unemploymentfor the following four decades: 1970-1979, 1980-1989, 1990-1999, 2000-2009. Please use theunemployment rate as the x-axis and the inflation rate as the y-axis in your plots. Add atrendline in each of your plot.(a) In which decade(s) can we observe a positive correlation between inflation and un-employment? In which decade(s) can we observe a negative correlation between inflationand unemployment? (4 marks)(b) Briefly provide one theory that can rationalize the negative correlation betweeninflation and unemployment. (3 marks)(c) Briefly provide one theory that can rationalize the positive correlation between in-flation and unemployment. (3 marks)