b) Agronomists, knowing that air pollution from phosphate mining damages nearby orange groves, have carefully tracked the loss in productivity of the orange groves with the output of the phosphate mine. The estimate of the cost to the owner of the orange grove is given as follows:

Tons mined per month	Marginal cost to orange groves
30	15
60	30
90	45

Note that this marginal external cost (mec) schedule isincreasingin phosphate production. What could explain that? Draw in the marginal external cost (from phosphate mining) to the orange groves curve by extrapolating from the three points in this table and extending the mec schedule to the range of output to 180 tons. Make this marginal cost curve linear. This is the marginal external cost from mining phosphate. What is the total cost imposed on the orange grove of mining 100 tons a month? At the equilibrium level of mining (the amount chosen by the phosphate firm) what is the marginal external cost imposed on the orange grove? What total cost does the orange grove suffer? At the equilibrium level of output of phosphate, what are the total social costs?

c) Now find the efficient level of output. This is the tons of phosphate where social marginal costs equal the social marginal value of phosphate, which in this case you can take to be the price of phosphate. (Speculate why the social marginal value of phosphate might be lower than the price.) Calculate external costs imposed by equilibrium level (tons of phosphate chosen by the mining firm) compared with the efficient level of output.

d) Consider a scheme of privatization in which the phosphate firm buys the orange grove. You should be able to show graphically or argue that in this case, the equilibrium level of output chosen by the phosphate firm is the same as the efficient (socially optimal) level of output. (Think about whether there are external costs when the phosphate firm buys the orange grove.). Why would this scheme of consolidating ownership not work in the case of a power plant, where emissions may impact a large number of private citizens?