Economics 103 Lecture # 15 Price Searching Here we are going to make another minor adjustment to our model. Rather than assume firms face a perfectly elastic (flat) demand curve, now we assume firms face a downward sloping demand. Why might that be? a. People are often ignorant of many things b. A firm may have a great location. c. Your product might be slightly different from the competition. d. Sellers might act strategically We’ll leave this one until next chapter. e. The firm might be a … monopolist. The KEY to understanding a price searching firm, is to understand the marginal revenue curve. Clearly marginal revenue is falling Recall when a firm was a price taker the marginal revenue curve equaled the price. Now marginal revenue is less than the price. For those of you who have had some calculus. Suppose the demand curve is given by the formula: p = a – b Q. If we multiply both sides by Q we get: PQ = aQ – bQ2 Note the left hand side is the Total Revenue. Now take the derivative with respect to Q. MR = a – 2bQ. So the marginal revenue curve falls twice as fast as the demand curve. Graphically we have: When MR=0, then TR is maximized, and the elasticity of demand is equal to –1. MR is negative in the inelastic region of the demand curve. This is the only adjustment we make for price searching. If the firm has ordinary cost curves, what price would the firm set? Notice the firm uses the same idiots rule of thumb This leads to a lower level of output, and a higher price than the price taking model. NB: The price searching firm DOES NOT maximize total revenue. Bono gets paid based on royalties, which are a share of the total revenues. A revenue maximizer wants to lower the price and raise the quantity to P’ and Q’. P’ Q’ Notice Bono never has said he wants to give his albums away. The same disputes arises between authors and publishers. In fact, between anyone who is paid a royalty vs. someone who has to bear the full costs. How much profit is this firm earning? We need to know the average costs. Suppose the average costs looked like this: Is this firm making a profit or loss? It would be making a profit equal to the shaded area. What if the average costs looked like this: Is the firm making a profit or loss, and by how much? The loss would equal the green area. If the price searching firm was making zero profits, then the average costs would look: This would have to be the equilibrium. If the price searcher was earning a profit, the price of the factor making it a price searcher would have to rise. The opposite would happen if the firm was making a loss. Natural Monopoly. For us this is a minor digression. What if a firm, had declining costs over the range of the demand curve? Why would costs look like this? How many firms could survive? If you forced the firm to set P=MC, what would the profit be?