The market for public goods

1.	To solve public goods problems:
	Step1: Determine the total demand for the product: Vertically sum the demand curves of all the consumers. This requires you to express price (P) as a function of quantity (Q) for each consumer and then add all the P's together to find the total price collected (PT). You can do this because everyone receives the same Q.     Step2: Solve for the optimal output of the public good (Q*): Set the total price (Pt) equal to marginal cost (MC) to solve for Q*.     Step3: Determine the prices to charge each consumer: Plug Q* back into each individual demand equation to find out how much each consumer should pay. These consumer-specific prices for a public good are referred to as Lindahl prices.

2.	Example: Consider farmers interested in cloud seeding to increase the rainfall for their crops.     Number of farmers: 4     Each farmer has the identical demand for cloud seeding: Q = 60 - 12.P     Marginal cost of cloud seeding: MC = 1/2.Q
	Step 1: Determine the total demand for the product:
	a.	Q = 60 - 12.P => P = ____________ (*)
	b.	4 farmers => 4.P = Pt = ____________ (**)
	Step 2: Solve for the optimal output of the public good (Q*):
		Pt = MC
	c.	(**) ____________ = 1/2.Q
	d.	Q* =  ____________
	Step 3: Determine the (Lindahl) price to charge each consumer:
	e.	P = ____________ (*)
	Notice that the Lindahl price collected from each of the 4 farmers is just enough to cover MC.

3.	Geometry:
	a.	In the diagram to the right: plot: (1) MC, (2) one of the individual demand curves, and (3) the total demand curve.
	b.	Label the equilibrium (1) Q*, (2) Pt, and (3) Lindahl price paid by each farmer.
	c.	Use the pattern "\\\" to shade in the consumer surplus (CS) and the pattern "///" to shade in the producer surplus (PS).
	d.	Complete the following table:
		Consumer surplus:   Producer surplus:   Total (market) surplus: