A firm in a perfectly competitive industry has patented a new process for making widgets. The new process lowers the firm's average costs, meaning this firm alone (although still a price taker) can earn real economic profits in the long run.

a. If the market price is $20 per widget and the firm's marginal cost curve is given by MC = 0.4q, where q is the daily widget production for the firm, and how many widgets will the firm produce?

b. Suppose a government study has found that the firm's new process is polluting the air and the study estimates the social marginal cost of widget production by this firm to be MCS = 0.5q. If the market price is still $20, what is the socially optimal level of production for the firm? What should the amount of a government-imposed excise tax be in order to bring about this optimal level of production?