1. Homework must be turned in on the day it is due. 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 is submitted as a typed .pdf file, no exceptions.  Untyped work will not be marked and will receive a mark of zero. You can draw a graph by hand, scan it, and include it as a figure in the 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.  (each question 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 consume the 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 a lower level of output under nonrandom monetary policy.

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

6. (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(c1,t,c2,t+1) = c + c 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 (c1(∗),c2(∗)) chosen by the individual in a stationary monetary equilibrium. How do (c1(∗),c2(∗)) 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 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) = c + c 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)