Problem Set 31. How can an elastic demand curve deter the formation of a cartel?2. Explain why collusive pricing is di?cult in one-period competition and easier when ?rms interactover a number of periods.3. Discuss factors that may facilitate collusion.4. Suppose that market demand is described by P = 100 ? (Q + q ), where P is the market price, Qis the output of the incumbent ?rm and q is the output of a potential entrant to the market. Theincumbent ?rm’s total cost function is T C (Q) = 40Q, whereas the cost function of the entrant isT C (q ) = 100 + 40q , where 100 is a sunk cost incurred to enter the market.a. If the entrant observes the incumbent producing Q units of output and expects this output levelto be maintained, write down the equation for the residual demand curve that the entrant ?rmfaces.b. If the entrant ?rm maximizes pro?t given the residual demand curve in a., what output q e willthe entrant produce? (Your answer should be a function of Q.)c. How much output would the incumbent ?rm have to produce to just keep the entrant out of themarket? That is, solve for the limit output QL . At what price will the incumbent sell the limitoutput?5. Please solve the Practice Problem 12.3 at page 282 from the textbook.6. Explain why predatory strategies do not work in an industry if no substantial sunk costs exist.7. Why is predatory pricing unlikely to occur when all ?rms are identical?8. Tiger-el is an upstream manufacturer of electric trains that sells wholesale to The Great Toy Store, the only such store in the area. Demand for the trains at the retail store in inverse form is P = 1, 000 ? 2Q, where Q is the total number of trains sold. The Great Toy Store incurs no service cost in selling the train. Its only cost is the wholesale price it pays for each train. Tiger-el incurs a production cost of$40 per train.a. What wholesale price should Tiger-el charge for its trains? What price will these trains sell forat retail? How many trains will be sold?b. What pro?t will Tiger-el and The Great Toy Store earn under the pricing choices you found inpart a.? What is the total pro?t of these two ?rms?c. Now assume Tiger-el and The Great Toy Store merge into one ?rm and they are maximizingjoint pro?ts. What would be the retail price and quantity sold in this case? Calculate the jointpro?ts.d. Compare the total pro?ts you ?nd in part b. and c.. Which one is greater? Why?10. Why are consumers and ?rms worse o? with successive monopolies upstream and downstream than when there is a single, integrated monopoly?11. Some products require special, custom-made trucks to transport by road. If a trucking companycontracts with a manufacturer for the transportation of such a product and invests in custom-madetrucks, how might this investment give rise to subsequent opportunistic behavior of the manufacturer,the trucking company, or both? How can such behavior be prevented?