作业代写｜ECOS3010: Assignment 1

这是一篇来自澳洲的关于货币计算相关的**作业代写**

Question 1-5. Answer True, False or Uncertain. Briefly explain your answer. (each question 4 marks)

- The lack of double coincidence of wants precludes people from using credit for transactions.

- Consider stationary allocations in the OLG model of money. Individuals consume the same amount of good when young and when old.

- The optimal monetary policy in the OLG model of money is to have deflation.
- In the Lucas price surprise model, a higher growth rate of money supply leads to a lower level of output under nonrandom monetary policy.

- The Lucas critique indicates that the government can use a random monetary policy to stimulate output.

- (10 marks) Consider the standard OLG model with money. Individuals are endowed with
*y*units of a perishable consumption good when young and nothing when old. There are*N*individuals in every generation. Each generation has identical preferences where

*u *(*c*1*,t**, c*2*,t*+1) = *c*1*/*21*,t *+ *c*1*/*22*,t*+1. There exists one asset in the economy – money. The money supply grows at a constant rate *z, *where *M**t *= *zM**t**−*1 and *z > *1. The new money created is used to finance government purchases of *g *goods per young individual in every period. The initial old are endowed with *M*0 units of money. In the following, we focus on stationary allocations.

(a) Find an individual’s budget constraints when young and when old. Combine them to 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 a stationary 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 function of *z *and other parameters in the model. (2 marks)

Now instead of being endowed with *y *units of the consumption good, individuals can supply labour *ℓ*1*,t *only when young. That is, the young supply labour *ℓ*1*,t *and consume *c*1*,t*,but the old can only consume *c*2*,t*+1. One unit of labour supply produces one unit of the consumption good. Each generation has identical preferences where

*u *(*c*1*,t**, c*2*,t*+1*, ℓ*1*,t*) = *c*1*/*21*,t *+ *c*1*/*22*,t*+1 *− **ℓ*1*,t**. *

(d) Find an individual’s budget constraints when young and when old. Combine them to form the individual’s lifetime budget constraint. (1 mark)

(e) Solve for the optimal consumption and labour supply (*c**∗*1 *, c**∗*2*, ℓ**∗*1 ) chosen by the individual in a stationary monetary equilibrium. (2 marks)

(f) How do (*c**∗*1 *, c**∗*2) depend on *z*? How does *ℓ**∗*1 depend on *z*? Briefly explain the intuition for your answer. (1 mark)

- (10 marks) Consider the OLG model that we develop in class. There are
*N*people in every generation. Each individual is endowed with*y*units of goods when young and nothing when old. Suppose that monetary authority prints fiat money at the rate*z*but now does not distribute the newly printed money as a lump-sum transfer to the old. Instead, the government distributes the newly printed money by giving each old individual new dollars for 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 them to form the individual’s lifetime budget constraint. (2 marks)

(c) What is the inflation rate *p**t*+1*/p**t*? What is the real rate of return on fiat money? (2 marks)

(d) Graph the stationary monetary equilibrium. Carefully label the axes and the optimal allocation. (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 regardless of the rate of inflation. Explain why inflation does not induce individuals to reduce their real balances of money in this case. (2 marks)

- (10 marks) Figure 7.1 and Figure 7.2 in Chapter 7 show the correlation between inflation 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 unemployment rate for Australia. Plot the correlation between inflation and unemployment for the following four decades: 1970-1979, 1980-1989, 1990-1999, 2000-2009. Please use the unemployment rate as the x-axis and the inflation rate as the y-axis in your plots. Add a trendline in each of your plot.

(a) In which decade(s) can we observe a positive correlation between inflation and unemployment? In which decade(s) can we observe a negative correlation between inflation and unemployment? (4 marks)

(b) Briefly provide one theory that can rationalize the negative correlation between inflation and unemployment. (3 marks)

(c) Briefly provide one theory that can rationalize the positive correlation between inflation and unemployment. (3 marks)

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