1) Suppose that real food prices rise unexpectedly and permanently. How does this change equilibrium wages?
This is a case where my intuition and my models are telling me different things, so I'll actually discuss my answer with anyone who cares to read this and ask for your feedback to help get my intuition or my models back on track.
My intuition and my newspapers say that when food prices rise, workers organize for higher wages. Cost of living increases, so wages should also. The whole theory that food price increases are inflationary relies on wages rising in response to increase the price of everything else. They've got to go up!
Then I jot down a simple model. People consume food and something else from their wages. They choose how much to work and it's basic economics to conclude that the marginal utility from consumption and leisure needs to be equalized. When the price of food goes up exogenously, consumers buy less of both goods, the marginal value of consumption increases, and they work more to compensate. This is an increase in labor supply.
At the same time, if people are buying less of both goods, firms don't need to produce as much, so they demand less labor. If labor supply increases and labor demand decreases, the only answer is that wages go down, not up.
Where am I going wrong?
Suppose I'm not going wrong, though. Suppose there are frictions in adjusting wages. Economic forces send the real wage down while social forces keep the nominal wage at the same level or higher. Unemployment goes up as a result. Either wages need to adjust down or the Fed needs to produce a little inflation (raising nominal food prices further, but not real food prices) to get us out of the recession. How does that sound?
One problem of course is that the last paragraph is a cheat. If I ask what happens to wages and simply assume that nominal wages are downward-sticky, it's not much of a fair question, is it? ... have to specify it better...