Question 4. AS Curve. Suppose firms follow a simple pricing rule. Firm i with
marginal cost MC sets its price $p_i = \mu MC$ where $\mu > 1$ is called markup
(price over marginal cost). Let $P_0$ be the initial average price level
(unweighted). Assume that only $\alpha \in (0, 1)$ fraction of firms can adjust their
prices.
a) Given the pricing strategy, what is the new unweighted average
price level after some of the firms adjust, $P_1$? It must be a function of
marginal cost, $\alpha$, and $P_0$. Unweighted means we take a simple average
of prices, without any adjustment by sales.
b) Suppose that the only variable cost of a firm is wage. Show that
the inflation is increasing with real wage.
c) Explain why an increase in marginal cost by 1 might increase the
price level more than 1.
d) Now assume that firms are following a more complex pricing
strategy. They take into account that they might not be able to adjust
their prices for a longer time. This means that they have to take into
account expected marginal costs in the future. What happens to the
optimal adjusted price of firm i if the expected inflation increases? Do
you expect it to go up or down? Why? What do you expect to happen to
markups (price over marginal cost)? What can you deduce from this
observation about the statement that \"the greedy firms are increasing
their prices more than cost and this causes inflation\"?
