(40 points) Get-the-lead-out manufactures generic \#2 pencils. Its cost function is C(q)= 1250+2q2, where q is the number of boxes of pencils it produces each quarter (throughout, quantities and prices refer to those of boxes of pencils; not individual pencils). The market demand curve for boxes of pencils (such as those made by this firm) is qD=10,00018p. (a) Find the firm's short-run supply curve. (b) Find the firm's long-run supply curve. (c) Suppose there are currently 150 pencil producers with identical cost functions. Given your answer to part (b), find the competitive equilibrium price, quantity, and profit per firm (assuming no additional firms enter). (d) Now suppose that new firms can enter, each able to duplicate the production process of the original firms, meaning they have identical cost functions as well. Find the long-run competitive market equilibrium price, quantity, and number of firms for this case. (e) The original 150 producers band together and lobby the government to exclude the new entrants, putting us back in the situation from part (c). In exchange, the government taxes the producers at $10 per box sold. Given this tax, i. What price will buyers now pay in equilibrium? ii. What price will sellers net in equilibrium? iii. How much revenue will the government raise with the tax? iv. How much dead-weight loss (DWL) does the tax create? What is the ratio of DWL created per tax-dollar raised