Consider an economy that incorporated the price of energy inputs (e.g. oil) explicitly into the AS curve. Suppose the price-setting equation is given by P=(1+θ)W α P E 1−a where PE is the price of energy resources and 0<α<1. Ignoring a multiplicative constant, W α P E 1−α is the marginal cost function that would result from the production technology, Y=N a E 1−a , where N is employed labour and E represents units of energy resources used in production. Assume that the inage-setting relation is given by W=P∨F(t,z) Make sure to distinguish between Pe, the price of energy resources, and Pv, the expected price level for the economy as a whole. a. Derive the aggregate supply relation. b. Let X≡P E /P, the real price of energy. Solve for P to obtain; P=p e (1+θ) a1 F(u,z)X α(1−a)
c. Graph the AS relation from part (b) for a given P ⊤ and α given X. d. Suppose that P=P. 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 reason it out. If P=P, 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 AD−AS diagram. 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. Pv) 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?