Let the production function be given by Y=*a*N, 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:

P=(1+µ)W/*a.*

Now consider the bargaining equation. I suppose that *a* shows up in
this expression as follows:

W=aP^{e}F(u,z).

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*.