Quantity Controls and Surplus Williamsburg is worried that the makers of tricorner hats are not making enough money to get by. A local official proposes the following plan. The city government will distribute permits to produce hats. You can only produce hats if you have a permit and there will only be enough permits for the production of 100 hats. The current number of hats being sold in equilibrium is 150 and the current equilibrium price is $20 a hat. (a) Suppose that each hat maker can make one hat and that the permits are randomly distributed. Use a graph of the supply and demand curves for tricorner hats to analyze the impacts of this plan on consumer surplus, producer surplus and total surplus. Assume that the market demand curve is linear with a negative slope and that the supply curve is upward sloping. (b) Are there any consumers who are strictly better off as a result of the new permit system? Are there any consumers who are strictly worse off as a result of the new permit system? Explain your answer. (c) Are all hat makers strictly better off as a result of the permit system? If not, which hat makers are now worse off? (d) Suppose that instead of the linear, downward sloping demand curve, demand is perfectly elastic: every visitor to Colonial Williamsburg is willing to pay $20 for a hat. If price rises above that, nobody buys hats. If the price drops below $20 demand is effectively infinite. How does this change your answers to parts a, b and c?