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# Cost and Pricing Homework Dr. Bowman We have been discussing various applications of economics in class. Some of the numeric problems below are...

Jones is a farmer in a competitive industry.Her cost function is TC=100Q.Demand is 1000-1/2Q.Find the long run equilbrium price and quantity.
10. The widget industry is currently composed of 10 identical firms. Each firm currently has one plant. It has cost: TC= 1600 + 50 Q + .25 Qsquared. (Q is output per year.) The long run costs for each firm involve a minimum average cost for each plant at \$90 for 80 units per year. It takes 5 years to change plant size. (No plants are currently under construction.) Demand is P=600-(1/4)Q. Initially there is competition. There are no barriers to entry or exit of firms in the widget industry. A) Please find the short run supply curve for a competitive firm. B) Please find the short run industry supply curve. C) Please find the short run industry equilibrium price(s) and quantity(ies). D) What are the long run price(s) and quantity(ies)? E) In the long run what price(s) and quantity(ies) are best (in a net benefit maximizing - explain) sense? What assumptions underlie your analysis here? F) What public policies might the U.S. effectively use to help achieve your answer in E? G) Suppose the industry as in D above becomes a monopoly. Find the long run equilibrium. H) In the general context of D and G above what is the range of equilibria that one might find under oligopoly? I) How much better off (in terms of dollars per month) are purchasers in D as compared to G? J) How much better off (in terms of dollars per month) are producers in D as compared to G? 11. The town of Podunk is considering putting in a public water supply. (People now have wells.) The system will cost \$200 per year. This system can handle any amount of water that the town might want. Separate from the system cost there is a \$1 per cubic yard of water cost in water purifying. The demand for public water in Podunk is P = 50 - .1 Q where Q is cubic yards of water per year. A) What price (and quantity) would maximize Podunk profits from the sale of public water? B) What price (and quantity) would be best for society in a net benefit maximizing sense? C) What public policies might help achieve your results in B. 12. Suppose that a movie theater owner faces the demand curve given by P=10-.001Q where P is the price of a ticket in dollars and Q is the number of tickets sold per week. Suppose that all the cost associated with the theater other than film costs do not vary with the number of tickets sold. A) What price will the theater owner charge if she must pay a fee of \$12,000 per week to rent the movie? B) What price will she charge if she must pay \$4 per ticket to the film distributor? C) What price will she charge if she must pay 80% of her revenues to the distributor? D) How much revenue will she get (\$12,000 per week rental) if she can perfectly price discriminate? 13. Jones is an oat farmer in a competitive industry. Her cost function for oats is TC = 100 Q. A) If the demand curve for oats is P = 1000 -(1/2) Q, please find the long run equilibrium price and quantity of oats. B) What price and quantity of oats is "best" for society (i.e., maximizes "net benefits")? Explain. What public policies might help achieve this? C) Suppose now that (in addition to the above conditions)
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