Let the production function be given by Y=aN, where Y is aggregate output, N is total employment and a is a measure of technology. The way to represent the price setting equation given this change in the production function is P=(1+µ)W/a. To understand why this is, recall that P is the price for one good. Under our theory this is equated to a markup over the marginal labor cost of the good. W measures the marginal cost of one hour of labor. So, if a=1 then the marginal labor cost of one good is W. But, if a jumps to, say, 2, then the marginal labor cost of one good is W/2, because it now takes the worker only 1/2 hour to make the good, at a labor cost of W/2. So, with the new production function, the price setting equation is:
Now consider the bargaining equation. I suppose that a shows up in this expression as follows:
The idea is that when a rises, the amount produced by a given worker goes up. The nature of the bargaining is that what the worker gets for his/her labors goes up in the same proportion as a.
1. show that an increase in a has no impact on the natural rate of unemployment (this is a good thing, since productivity has been rising constantly for a couple hundred years and unemployment has not shot off to zero or unity).
2. Show what happens to the AS curve after a rise in a.
3. Indicate the short run equilibrium after a rise in a, and the medium run equilibrium, in the AD-AS diagram, and in the IS-LM diagram.
4. What happens to unemployment in the short run equilibrium as a result of an increase in a.
5. What happens to I, i, P after the rise in a.