Imagine that the current price of waste disposal is $0.025/lb and the average wa
ID: 1179857 • Letter: I
Question
Imagine that the current price of waste disposal is $0.025/lb and the average waste disposal is 2.40 lb/p/d. When the price was previously $0.01/lb, the average waste disposal was 2.52 lb/p/d. Assume that the marginal social cost of waste disposal is $0.06/lb, that marginal social costs are constant with respect to quantity, and that the town has a population of 100,000. Fitting a linear demand curve to the two observed points, calculate the annual net benefits of raising the price of waste disposal to $0.05/lb.
Explanation / Answer
1. The social cost of not setting pricing equal to the social marginal cost is given by the area between the marginal social cost curve, which in this exercise is a horizontal line (p = $0.06/lb), and the marginal social benefits curve (the demand curve) where quantity ranges from the socially optimal quantity to the quantity at the current price. Pricing closer to the social marginal cost reduces this area. The (net) social benefit equals the reduction in the area.
Assuming a linear demand curve through the observed points, as the price rises from $0.25/lb to $0.50/lb,
quantity falls by 0.20 lbs/p/d from 2.40 lbs/p/d to 2.20 lbs/p/d.
The gain in benefits equals the total reduction in social cost [($0.06/lb)(2.40 lbs/p/d-2.20 lbs/p/d) = $0.012/p/d] minus the lost benefits given by the area under the demand curve [(.5)($0.025)(0.2 lbs/p/d)+($0.025)(0.2 lbs/p/d) = $0.0045/p/d.
If the town's population is 100,000 people, then the annual net benefits are $0.0045x100,000x365 = $164,250.