Prof. Bryan Caplan

Econ 816

Spring, 2000


HW#3 Answers


Part 1: Mathematical Problems

1.  Romer, 5.2.


a.  The result is that the LM curve becomes a flat line horizontal at the interest rate peg .


b.  If the LM curve is horizontal at the interest rate peg, then the monetary authorities must be adjusting M 1:1 in response to any change in P.  Therefore, changes in P have no effect on AD.  In consequence, the AD curve is vertical.


2.  Romer, problem 5.4.


a.  As in the previous case, there will be a horizontal LM curve.  The mechanism is however a little different: not only is the LM curve horizontal, but by assumption it is insensitive to changes in M.  (If people are willing to change their money holdings without any change in the interest rate, then changes in M or P will have no impact on the interest rate!)  The consequence is the same as above: the AD curve becomes vertical.  If the AS curve is vertical as well, then there may still be underemployment if the AD curve is vertical to the left of the AS curve; shifting the AD curve using fiscal policy would increase output.


b.  So far we have been making the traditional assumption that P enters only the LM curve, not the IS curve.  Once P appears in the IS equation, there is a second channel for a fall in P to increase AD.  As a result, the AD curve is now downward sloping!  Assuming that the quantity demand at P=0 exceeds potential output, there can now be full employment at any level of demand.


3.  Romer, problem 6.15.


a.  First, plug the AD equation into the p* equation to get:


p*=p+j(m-p).  Then plug in p=fp* and m=m', to get:




Solving for p*:



p will therefore be given by:




y will similarly be:




b.  The firm's incentive to adjust its price is:




Note that when j=1, the above expression reduces to Km'2, which is not a function of f.  So you can just draw Kp*2 as a horizontal line with f on the x-axis.


When f=0, Kp*2=Kj2m'2.  So the larger j is, the greater the incentive to change prices at f=0.


When f=1, Kp*2=Km'2 regardless of the value of j.


Checking the derivative of K{jm'/[1-f(1-j)]}2 wrt f, it can be seen that the function is increasing in f if j<1, and decreasing in f if j>1.


So your graph should show a horizontal line Km'2 for j=1.  It should show a curve that begins above this line for j>1, and decreasing as f increases until it intersects the horizontal line at f=1.  Conversely, for j<1, your curve should begin below the horizontal line, and increase as f increases until it intersects the horizontal line when f=1.


c. Kp*2 is an increasing function for j<1, and a decreasing function for j>1.  Thinking about this intuitively, if Kp*2>Z, then more people want to change price; if Kp*2<Z, then fewer people want to.


Therefore, when j>1, the more people change price, the smaller the benefit; the fewer people change price, the larger the benefit.  As long as Z "cuts" the benefit curve, you will have to have an interior solution between 0 and 1 at the point where Z and the benefit curve intersect.


On the other hand, when j<1, the more people who change price, the larger the benefit; the fewer people who change price, the smaller the benefit.  Therefore the equilibrium where Z and the benefit curve intersect is unstable; a slight perturbation means that you tend to go to f=1 or f=0.


Part 2: Analytical Problems


I won't provide sample answers here, but I do have some general and question-specific comments.


1.  What is the least implausible mechanism for policy to work in an RBC model?  Why?  Do Braun and McGrattan appeal to this mechanism in their analysis?  Are they successful?


Many people just summarized the standard RBC channels without indicating which they found most plausible (=least implausible). 


2.  Briefly explain (TOTAL of 1 page):

a.  Why the uninsured competitive equilibrium is sub-optimal in the Rogerson model.


The main intuition to have here is that with identical agents, expected utility maximization requires equal consumption for everyone.


b.  Why King and Plosser fail to prove that nominal money and real output are correlated in their model.


Most people had no problem with this.


3.  Briefly describe one interesting/unusual monetary episode from Friedman and Schwartz, and outline your best explanation for what happened.


There were diverse answers here.  You got a high score if you not only summarized an episode, but tried to explain why it was interesting.


4.  Several critical replies to ADP follow their article.  Which objections are most telling?  How might ADP reply? 


Most of the answers here were good.