Problem: 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 + y^2 if y > 0 and c(y) = 0 if y = 0. The government imposes a lump sum tax of $300 on each firm in the industry. Firms can only avoid this sword 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!
Required:
1. What is the price and output per firm in the before-tax world and in after tax word of Westeros?
2. 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?