Suppose a firm produces charcoal in a perfectly competitive charcoal industry where the price of charcoal is $20 per ton. This particular firm, however, enjoys a competitive advantage over other firms because it is located on a scenic river that enables it to have relatively low production costs. Specifically, the firm's Total Costs are given by TC(q) = 0.2q2 + 200 and its marginal costs by MC(q) = 0.4q where q represents the firms charcoal output in tons per day.

a. What will the firm's daily output of charcoal be in this situation and how much will it earn in profits?

b. Suppose there is an eyeglass manufacturer downriver from this firm that incurs extra costs per day of 0.1q (where again q is the output of the charcoal firm). What are the social marginal costs of charcoal production and what is the socially optimal output level for this firm?

c. If the government wished to impose a tax on the charcoal firm to cause it to produce at the socially optimal level of output, what should that tax be (per ton of charcoal)?

d. If the government imposes that tax calculated in part c, will the charcoal firm continue to produce in this location?

e. Graph your solutions to this problem.