Problem 1. A rms sells hospital-grade disinfectant in a perfectly competitive market for $60 per gallon. The rm's unavoidable xed costs are $1000 this month and the rm can produce up to 50 gallons per month. The marginal costs when producing Q gallons are M 90' (Q) = 10 + 2Q for all Q between zero and 50. (1.1) Write a mathematical expression for total revenue TR(Q), average revenue AR(Q), total cost TC(Q), variable cost VC(Q), average xed cost AFC (Q), average variable cost AVG (Q) and average total cost ATC (Q) as a function of quantity Q. (1.2) Use your favorite spreadsheet software to plot a graph ofMgC(Q), AVC(Q), AFC(Q), ATC(Q), and AR(Q) for Q between zero and 50. (1.3) If the rm wanted to maximize total revenue, how many gallons of disinfec- tant should it produce? What would be the prots? (1.4) What quantity should the rm produce in order to maximize prots? (1.5) At the prot-maximizing level of output, how do marginal revenue and marginal cost compare? (1.6) Suppose that unavoidable fixed costs suddenly double. How should the rm change production to account for this sudden increase in cost? (1.7) Suppose the marginal cost increases by $2 at every level of production. How should the rm alter production to account for this sudden increase in cost? Problem 2. Assume there are ten firms operating in a perfectly competitive market for a product. Each firm has fixed costs of 4 and variable costsVC(Q) = Q2. (2.1) Find TC(Q), MgC(Q) and ATC(Q) for a representative firm. (2.2) What is the short-run supply curve for a single firm? And for the entire market?{2.3) Suppose the market demand curve for this product is given byQ : 2E] P . Find the market price P that makm the quantity demanded equal to the quantity supplied in this market. How many units are sold at this price? {2.4) At the equilibrium price you found above, what is the output and profit for each firm? {2.5) If there are no barriers to entry and exit in this industry, do you expect pricesl to remain stable, increase or decrease in the future? Why? {2.6) What price you expect to see in this market in the long run? How much will each firm produce at this price? Pl'Oblem 3- Fred's Fine Fried Dough, a successful New Orleans franchise chain, has expanded into upstate New York State. Each franchisee pays Fred a xed annual fee for the right to be a Fred's location, and otherwise controls all other aspects of the business. Each location has a total cost function for dough that has strictly increasing marginal cost. (For simplicity you may assume that all factors of production are variable, and that the franchise fee is refunded if the franchisee elects not to operate a restaurant. Also, since there are no data/ numbers provided, there is a limit to how specific an answer you can give. Keep it simple and diagrammatic.) {3.1) Draw total, marginal and average cost functions that might describe a Fred's location. {3.2) Assume customers view the many Fred's locations as identical, and the fran- chises are perfect competitors in the fried dough market. Draw an individual franchise's supply curve. {3.3) The 37 Fred's locations in upstate New York all have the same costs. Draw the market supply curve for fried dough. {3.4) Being one of the 37 Fred's franchises has turned out to be very protable. Along with your market supply curve, draw a market demand curve consis tent with such protability. What is the fried dough price? {3.5) How many of the 37 locations operate in equilibrium? {3.6) How much does each location produce? {3.7) Fred does not plan to change the franchise fee for nem year, but does intend to let anyone who wants to pay the fee and open a Fred's franchise in upstate New York. Comparing this year with next year, what will happen to the number of franchises