Microeconomic Theory 11th Edition by Walter Nicholson,Christopher Snyder

Exercise 1

A firm in a perfectly competitive industry has patented a new process for making widgets. The new process lowers the firm's average cost, meaning that 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 is given by MC= 0.4 q , where q is the daily widget production for the firm, 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 estimates the social marginal cost of widget production by this firm to be SMC= 0.5 q. If the market price is still $20, what is the socially optimal level of production for the firm? What should be the rate of a government-imposed excise tax to bring about this optimal level of production?
c. Graph your results.