Lindahl Pricing and Equilibrium free essay sample

Lindahl Pricing and Equilibrium – Proof of Pareto Optimality A Lindahl equilibrium is a method for finding the efficient level of provision for public goods. Recall that for public goods, in equilibrium all agents consume the same quantity but may face different prices1. As it is framed in our textbook, the Lindahl equilibrium occurs when the perunit price paid by each agent sums to the total per unit cost of the public good. The Graph We start with a good ol’ fashioned demand curve for a public good. The lower the price of the good, the more Person 1 wants to consume. Now imagine that the dashed horizontal line is the full price of the good. At this point, the demand curve makes it look like Person 1 will demand very little. But what if rather than the price dropping, the percentage of the price he have to pay goes down? As far as Person 1 is concerned, this is equivalent to the price he sees going down, so he’ll demand more. We will write a custom essay sample on Lindahl Pricing and Equilibrium or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Full price Price * 50% Price * 25% Price * 0% D1 Qfull price QPrice * 50% QPrice * 25% Q Now lets look at another demand curve (Person 2). This person sees the vertical axis flipped the other way around, with the full price on the bottom and percentage decreasing as one moves upward. Like Person 1, Person 2 will demand more as her observed price goes down. Price * 0% D2 Price * 50% Full price Qfull price 1 QPrice * 50% Q This differs from equilibrium of private goods, which instead has all agents viewing the same price with the possibility to consume different quantities. Prepared by Nick Sanders, UC Davis Graduate Department of Economics 2006 Again, note that here Person 2’s observed price going down means we move further up the vertical axis. Equilibrium is when both of these people demand the same amount of the public good. This happens when the two demand curves intersect each other. If we draw a line over to the price axis from that point of intersection, we get the percentage share for each agent that is required to get that price. Person 2 P*55% Full price = P Person 1 P*45% Q* D2 D1 Q So Person 1 is paying P*45% per unit, Person 2 is paying P*55% per unit, and the economy produces Q* units. Here we have a Lindahl equilibrium, and the corresponding prices are called Lindahl prices. But is it a Pareto Optimal (PO) equilibrium? As they say in mathematical circles, Q. E. D. 2 ! The Issues As with all good ideas in economics, there are some issues with real world applications of the Lindahl equilibrium. For one, it assumes that we know each individuals preferences. What if people intentionally hide their true willingness to pay? This starts getting into the â€Å"free rider† problem issue again, where people decide to let others cover the costs, but reap the benefits themselves. Even if we DID know exactly what everyone’s preferences were, things would still get significantly more complicated as there were more and more people involved in the discussion. It’s one thing to get two people to agree on some provision of a public good, but getting a city of 100,000 people to do so is just plain nuts3. 2 It’s an abbreviation for the Latin phrase â€Å"quod erat demonstrandum†, or â€Å"that which was to be demonstrated†. It basically means the proof is done . . . use it to impress your friends and family. 3 Basically, that means we’re dealing with up to 100,000 prices for just one good. This makes finding an equilibrium much, much harder. Prepared by Nick Sanders, UC Davis Graduate Department of Economics 2006