The competitive sword manufacturing industry in Westeros has 10,000 identical firms. For each firm in the industry, the long run cost of producing y units of output is c (y) = 100 y2 if y > 0 and c(y) = 0. The government imposes a lump sum tax of $300 on each firm in the industry. Firms can only avoid this sward tax by going out of business. We can assume free entry and exit into this industry. Furthermore demand is vertical; the knights of Westeros need their swords!
a. What is the price and output per firm in the before-tax world of Westeros?
b. What is the price and output per firm in the after-tax world of Westeros?
c. Did the tax have any affect on total output produced? How were prices and the number of firms affected? Be specific. Finally, are the sword manufacturing firms that are producing after the introduction of the tax worse off?