Question

P (S) 50 45 40 35 30 25 20 15 o 20 30 40 50 60 70 80 90 100 110 120 130 140 150 -5 -10 Suppose that there are 5 people with identical preferences around a pure public good. For each individual (i e {1, 2, 3, 4, 5]) the Private Marginal Benefit (PMB,) from a pure public good is given by PMB, 10-0.1G, where G is the quantity of the pure public good. 1. Draw the Private Marginal Benefit curve for a typical individual and label it PMB, 2. Draw the Social Marginal Benefit curve from the pure public good and label it SMB. Suppose that the marginal cost of providing the pure public good is a constant $15. Draw the social marginal cost curve and label it SMC. 3. 4. The optimal level of the public good is G 5. A pure public good is non-excludable. How much of the pure public good will be (be precise) provided by the private marketplace? GE

Answer 1

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The PMB represents the private Marginal Benefit curve, SMB represents the Social Marginal Benefit curve and SMC represents the social marginal cost. Since the preferences of the consumer are identical, thus, market demand for pure public good id given by the vertical addition of the individual demand curves of individuals.

The optimal level of public good occurs at the point where market demand curve of pure public good intersects the marginal cost curve, thus, 50 - 0.5 G = 15, thus optimal level of G = 70 units.

The private market will provide the good at the point where marginal revenue from the good = marginal cost, thus MR = 50 - G = 15, thus G = 35 units.