EC 110 THANKSGIVING WEEK HANDOUT Problems SOLUTIONS In this problem set we will do two things. First, we look at another monopoly situation, that can be treated like a natural monopoly and then we move on to a new market structure, monopolistic competition. 1. A company is considering the possibility of constructing a bridge across the Black Warrior River in an isolated area but where there is a lot of traffic. The bridge will cost $2 million dollars to build but there are no maintenance costs and (making an heroic assumption) the bridge will last forever. The table below details the demand for bridge crossings over the lifetime of this bridge. Price per Crossing Number of Crossings (in Thousands) TOTAL REVENUE MARGINAL REVENUE $8 0 0 ------- $7 100 $700,000 7 $6 200 $1,200,000 5 $5 300 $1,500,000 3 $4 400 $1,600,000 1 $3 500 $1,500,000 -1 $2 600 $1,200,000 -3 $1 700 $700,000 -5 $0 800 $0 -7 a. If the bridge is constructed, what is the profit-maximizing price? Assuming that it is/has been constructed, since there are no maintenance costs—no variable costs—this implies that marginal cost (MC) is $0. In this case, so long as marginal revenue (MR) is greater than zero, then the price should be lowered and output increased. Another way to say this is that you want to choose the output that maximizes total revenue. At output levels up to 400, MR > 0 but at output levels higher than this, MR < 0. So the profit maximizing output would be at Q = 400 (or 400,000). b. What is the efficient level of output? Would the bridge company produce this output? Why or Why not? Efficiency occurs where the output is produced at which P = MC. Since MC = 0, then the efficient price would also be zero, which maximizes the number of crossings. A private, profit maximizing bridge company would never willingly choose to do this. This is another version of the NATURAL MONOPOLY situation, where the natural monopolist will never willingly choose to produce the efficient output level because it cannot cover its costs at that output level (P < LRAC here when P = LRMC). c. Given the circumstances, would the company build this bridge? The answer to this is easy—NO. Since the company would never recover its initial investment of $2 million with its revenues, even at the profit maximizing output, the firm would not choose to build the bridge. d. Is there an alternate way to have this bridge built and operated? If so, what should the price be? Yes. It could be built by government. We would have to determine whether the total benefits are greater than the total costs to do this (to justify the expenditure). Assuming government wants to have efficiency, it would charge a zero price. This is the price charged for most bridges, though there are toll bridges. [note: if one could assume that price is equal to actual willingness to pay or MB, then you could calculate total benefit, but this is well beyond the scope of this course. It might also be possible to cover the costs of construction if price discrimination was feasible]2. Kevin owns a personal training gymnasium in Orlando. The above figure shows the demand and cost curves for his firm, which competes in a monopolistically competitive market. Determine Kevin’s output, price and profit from the diagram. This is another application of finding where MR = MC; here that is at an output of 4 units per day. Kevin will charge a price of $60, and from the diagram we can see that the cost per unit (from ATC) is $40, so profit per day will be (60-40)*4 or $80. Finally how will the situation here differ, in the long run, from that of a typical monopoly? As we can see, the answers and the method for finding here do not differ in any meaningful way from that in a standard monopoly situation. This is important to point out. But it is also important to point out that with the market being characterized by monopolistic competition there is something that affects the outcome—in the long run—that cannot be shown in the diagram. That is because here there are no entry barriers, so other firms can enter the market and produce a similar product; this market is also characterized by product differentiation, so that no firm produces a product identical to that produced by another firm. Yet the differences are small; sometimes these differences are only that of the perception of the product by the customer—something that the firm would like to promote. Most firms will, in fact, spend money to try to enhance the customer’s awareness of these differences. Entry by others and the costs of differentiation results in a long run outcome essentially like that in a perfectly competitive market (i.e., zero economic profit), except that price is above marginal cost. We can think of this as the price of product differentiation, or the price of variety. Here’s an example of how the long run curve for Problem 2 might look. This is not the only way to construct it, but it does result in the outcome we are looking for: P = AC, so profits are zero, but price is above MC.Here, the price would be approximately $60 and the quantity would be lower—at about 3 per day. This is due to entry by other firms (reducing the demand for this firm). Based upon the original diagram, the quantity price may be lower—perhaps somewhere in the neighborhood of $50 or lower (maybe $48, depending upon the slope of the new demand curve; that is, whether the slope was the same or if it changed, and was