Macroeconomics 5th Edition by Olivier Blanchard

Exercise 13

Adding energy prices to the AS curve
In this problem, we incorporate the price of energy inputs (e.g., oil) explicitly into the AS curve.
Suppose the price-setting equation is given by
where P E is the price of energy resources and 0 a 1
Ignoring a multiplicative constant,
is the marginal cost function that would result from the production technology,
where N is employed labor and E represents units of energy resources used in production.
As in the text, the wage-setting relation is given by
Make sure to distinguish between P E , the price of energy resources, and P e , the expected price level for the economy as a whole.
a. Substitute the wage-setting relation into the price-setting relation to obtain the aggregate supply relation.
b. Let
the real price of energy. Observe that P × x = PE and substitute for P E in the AS relation you derived in part (a). Solve for P to obtain
c. Graph the AS relation from part (b) for a given Pe and a given x.
d. Suppose that P = P e. How will the natural rate of unemployment change if x, the real price of energy, increases [Hint: You can solve the AS equation for x to obtain the answer, or you can use your intuition. If P = P e , how must F(u, z) change when x increases to maintain the equality in part (b) How must u change to have the required effect on F(u, z) ]
e. Suppose that the economy begins with output equal to the natural level of output. Then the real price of energy increases. Show the short-run and medium-run effects of the increase in the real price of energy in an AS-AD diagram.
The text suggests that a change in expectations about monetary policy may help explain why increases in oil prices over the past few years have had less of an adverse effect on the economy than the oil price shocks of the 1970s. Let us examine how such a change in expectations would alter the effect of an oil price shock.
f. Suppose there is an increase in the real price of energy. In addition, despite the increase in the real price of energy, suppose that the expected price level (i.e., P e ) does not change. After the short-run effect of the increase in the real price of energy, will there be any further adjustment of the economy over the medium run In order for the expected price level not to change, what monetary action must wage-setters be expecting after an increase in the real price of energy