$10.00 Please help me sovle this Game theory problem
- From Economics: Game-Theory
- Closed, but you can still post tutorials
- Due on Nov. 05, 2009
- Asked on Nov 02, 2009 at 6:30:30PM
Q:2. Rules vs. Discretion in Monetary Policy (Polak) Suppose the government of
country A can choose the inflation level, p. The nominal wage increase, W,
however, is not set by the government but by an employer-union federation. This
federation would like real wages to remain unchanged; that is, if they could, they
would set W = p. Specifically, given W and p, the utility of the federation is
given by uf(W,p) = 100 - (W – p)2. For reasons that we do not need to go into
here (read about the Phillips curve on Wikipedia if you want an intuition), real
output in country A is y = 30 + (p – W). The government likes output more than it
dislikes inflation. Specifically, given y and p, the government’s utility is ug(y,p) =
y – p/2 – 30. (Notice, substituting in for y, the government’s utility is just p/2 –
W.)
Our game is played as follows. First the federation chooses a nominal wage, W.
Then the government observes W and chooses an inflation level, p. Then thegame ends with each player receiving payoffs given by their utilities. Assume that
neither W nor p can be less than 0 or larger than 10.
a. What will be the government’s strategy in a Subgame Perfect
Equilibrium? [Hint: You do not need calculus for any part of this problem]
b. Using backward induction and your answer from part (a), find the level of
inflation p, nominal wage increase W, and (hence) output y that will occur
in the Subgame Perfect Nash Equilibrium. (If you’ve had macro, it is
worth thinking about the relationship here between backward induction
and ‘rational expectations’.)
c. Suppose that the government could commit to a particular inflation rate
before the federation made its choice. What inflation rate would the
government like to commit to? How would the utilities of the two players
change from case (a)?
d. In the real world, how have governments attempted to commit to
particular inflation rates (i.e., monetary policies)?
