Question

Consider the demand for a public good estimated for two sets of consumers: P1 = -0.5Q...

Consider the demand for a public good estimated for two sets of consumers:

P1 = -0.5Q + 10

P2 = -0.25Q + 5

where P is the price that each consumer is willing to pay at difference levels of quantity. The cost of providing one additional unit of this public good is $4 (e.g., marginal cost (MC) = $4)

a) Derive the equation of the market demand curve for this public good. Hint: Remember that in this case you have to add vertically which amounts to adding equations 1 and 2 together.

b) Draw each individual demand and the market demand curve on the same graph. (Price (P) on the vertical axis and quantity (Q) on the horizontal axis.) Clearly label each curve. Make sure to include the value of the horizontal and vertical intercepts. Hint: You should have three curves on the graph.

c) What is the allocative efficient level for this public good? Hint: Remember that at the allocative efficient level, the marginal cost (MC) of providing this good equals the market demand for this good.

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