Lindahl Pricing and Equilibrium – Proof of Pareto Optimality

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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. 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...
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