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Economics 422 Winter 2010 Monetary Economics Allen Head Assignment

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Economics 422 Winter 2010 Monetary Economics Allen Head Assignment Powered By Docstoc
					Economics 422                                                                        Winter 2010
Monetary Economics                                                                    Allen Head


                                       Assignment 4
                                (Due Wednesday, April 7th)



 1. Consider the economy from parts 1d. and 1e. of Assignment 3:

 • There is a constant population (Nt = N for all t) of overlapping generations of three-
   period lived agents with preferences:

                      u(c1,t , c2,t+1 , c3,t+2 ) = ln c1,t + ln c2,t+1 + ln c3,t+2


 • Agents are endowed with 3 units of consumption good when young.
 • Agents can convert one unit of consumption good into one unit of capital at any point
   in time. Two periods after its creation, each unit of capital produces x = 1.5 units of
   consumption good.
 • The government collects seignorage by increasing the stock of fiat money at gross rate
   z = 1.25 each period.
 • Individual agents are unable to commit to repay loans, and thus are unable to borrow
   against future capital income. There are, however, a large number of “banks” who
   can commit to their depositors. These banks behave competitively.



    a. In Assignment 3 you derived the stationary equilibrium of this economy (see the
       answers that were distributed). What are the value of fiat money, rate of inflation,
       and level of seignorage collected in this equilibrium?

    b. Suppose that the government sets up a central bank, and that the central bank
       imposes a requirement that banks hold reserves in fiat money equal to 10% of the
       value of their deposits. Find the stationary equilibrium of this economy.

     c. What are the value of fiat money, rate of inflation, and level of seignorage collected
        in this equilibrium?

    d. Is aggregate consumption higher or lower in the equilibrium with a reserve require-
       ment than in the one without (i.e. the equilibrium you derived in Assignment 3
       part 1d.)? What accounts for the difference?



                                                1
2. Consider a version of the “worker-entrepreneur-bank” economy discussed in class and
   in Chapter 9 of Champ and Freeman. To avoid writing out all of the details of the
   basic environment here, I refer you to pp. 172-174 of the text (recall that it is available
   online).

   Consider a slightly different version of this economy that differs from the one described
   in Champ and Freeman in the following ways:

     i. Rather than being constant, the population grows at gross rate n = 1.5.
     ii. The monetary authority collects seignorage by increasing the money stock at rate
         z = 1.2
    iii. The one-period rate of return on capital equals x = 1.5.
    iv. The cost incurred by a worker of transacting with a bank is equal to ϕ = .25
        units of consumption good.

    a. Draw a diagram depicting a worker’s return on deposits. At what level of savings
       does it become worthwhile to make a deposit with a bank rather than holding
       fiat money?

    b. What will happen to the money multiplier if...
           i. the transaction cost, ϕ, falls?
           ii. the inflation rate, z, rises?

   (Its probably easiest to answer part b. using a diagram.)




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