Sleeping bag production for the Sleepwell Company has cost C(Q) = Q3 - 10Q2 + 35Q + 196. The marginal cost curve for their production is MC(Q) = 3Q2 - 20Q + 35.
(a) Identify both the shutdown point and the minimum average cost. (Hint: if you have access to a spreadsheet program, you may find it easier if you put into it the formulas for AVC, AC, and MC for values from Q = 1 to Q = 10.)
(b) The price of a sleeping bag is currently $67. How many sleeping bags will Sleepwell produce? What will be its profits?
(c) The market for sleeping bags is competitive, with multiple producers. Because sleeping bag technology is commonly known and there is no government rule against using that technology, all the producers operate with the same cost curves. The demand curve for sleeping bags is QD = (1001 - 3P)/25. How many sleeping bags are people willing to buy at the current market price? How many producers do you estimate there are in the industry? Is the market in a long-run equilibrium? Why or why not?
(d) A new sleeping bag company enters the industry, and the price of sleeping bags drops to $42 per bag. How many sleeping bags are people willing to buy at the current market price? How many sleeping bags will each company make? Is the market in a long-run equilibrium? Why or why not?
(e) Regulators are concerned that the large number of people visiting parks and wilderness will cause damage to ecosystems. They decide that one way to keep people out is to limit the number of sleeping bags produced; without them, fewer people will stay overnight in the areas. They declare that no producer can make more than 5 sleeping bags, and no new sleeping bag plants may come into production. What price will lead to the quantity demanded equaling the quantity supplied under this rule?
(f) What will Sleepwell's profits be, with this new price and a quantity of five sleeping bags produced?
(g) Does government regulation of sleeping bag production increase or reduce profits for sleeping bag producers? Why?