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)
u (c1,t, c2,t+1) = c1/21,t + c1/22,t+1. There exists one asset in the economy – money. The money supply grows at a constant rate z, where Mt = zMt−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 M0 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 ℓ1,t only when young. That is, the young supply labour ℓ1,t and consume c1,t,but the old can only consume c2,t+1. One unit of labour supply produces one unit of the consumption good. Each generation has identical preferences where
u (c1,t, c2,t+1, ℓ1,t) = c1/21,t + c1/22,t+1 − ℓ1,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)
(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 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 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)
(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)