Part 111 Taxis and Ubers (30 points) 'We begin with a simple problem of demand and supply in the taxi market. It is rush hour on a Friday. [t's raining. A lot of people want taxis. We want to first find out how the market works when only taxis exist and prices are free to adjust. o The demand curve can be summarized by the equation P = 100 Q7. & The supply curve of taxi drivers to the market can be summarized by P = Q5. A. Draw a figure that shows demand and supply for taxis, with price P on the vertical axis and quantitites @ on the horizontal axis. B. If this were a perfectly free market, what would be the equilibrium price for a ride and the number of rides taken? C. In your figure, identify consumer surplus and producer surplus and label them. We now note that the price for taxi rides is not set in a free market, but instead by the Taxi and Limousine Commission (TLC) of New York. The TLC in our example sets the price at Pp = 40. D. At the TLC-set price, what are demand and supply? Is there excess demand or excess supply, and of what magnitude? (Hint: with the price given from the TLC, you should be able to figure out quantity demanded and quantity supplied separately, since prices don't necessarily move to equate the two). E. Draw a new figure to illustrate your results. Is there rationing of drivers who can't find riders or potential riders who can't find taxis? F. In your figure, identify consumer surplus and producer surplus and label them (you can assume that taxis are always obtained by the consumers who value them most highly). Have these gone up or down relative to the free market equilibrium? Now we consider what happens if Uber enters the market and also begins to offer rides. We are going to consider a similar rainy Friday during rush hour when demand for rides is high. e The inverse demand curve for rides is still given by the equation P = 100 Q. e We assume that (a random) half of the taxi drivers have left to work for Uber. Since there are fewer taxi drivers, the supply curve for regular taxi drivers shifts to P = 2Qf and there is a similar curve for Uber drivers Py = 2Q. Drivers cannot switch between the two on this day. G. The TLC continues to impose the price Py = 40 for taxi rides, but is not able to control the price for Uber rides. Taking account of the new taxi ride supply curve, how many taxi rides will be provided? The TLC sets the price for the taxi drivers and it is set long before it knows demand. So it is just fixed. By contrast, Uber will try to set a price that maximizes its profits. e We have already said that the supply curve for Uber drivers is given by Py = 2Qf, where Py is what Uber pays to drivers. e Uber, though, is free to pay drivers one price and charge riders another (higher) price. We will assume that from the viewpoint of Uber, the Uber driver supply curve is also Uber's marginal cost curve (we ignore any potential monopsony power). Thus we need to distinguish the price that Uber charges riders, which we label Py from what it pays drivers, Py. e From answer G above, you have already calculated how many taxi rides will be provided at the TLC price P = 40. Let's call this number Q. Assume that Uber takes that number as given. Then we can derive a residual demand curve facing Uber that is exactly the same as the original demand curve, but adjusted for the fact that some of the demand is already taken care of by taxis. H. Write down the residual demand curve that Uber faces, once it knows how many riders are served by taxis. I. Write total revenue (Price x Quantity) as a function of the number of rides provided. J. Derive an equation for marginal revenue for Uber. K. Relative to the residual demand curve, Uber is just a monopolist, so equates marginal revenue and marginal cost. What price for the ride Pp, will it set? How many rides will it deliver? How much will each Uber driver earn, ie. what is P (remember the payments on the supply curve for Uber drivers we are taking as Uber's marginal cost)? L. Draw a figure illustrating the original demand curve, Uber's residual demand curve, and the equilibrium price and quantity of Uber rides. M. How do Uber's price and quantity compare to those of the taxi? N. Are Uber drivers in this example paid more or less than taxi drivers? O. Compare the producer surplus of Uber versus the owners of the taxis