SI. Four large used-car dealers compete for customers in a city where demand for used automobiles is constant at about 800 cars per month. By an implicit agreement, the dealers set comparable prices on their cars, with the result that price wars and competitive discounting are extremely rare. All dealers claim to have the lowest prices, but the facts say otherwise. The average (variable) cost of a used car to the dealer (procuring and readying it for sale) is 82,400. The average sale price per car is $4,000. The dealers do compete with respect to the number and types of cars in their showrooms. The typical prospective buyer visits a number of dealers looking for the \"right\" car. The greater the number of cars a dealer has available, the better is its chance of melting a sale. In fact, a particular dealer's share of the total market is proportional to the number of cars it holds in its showroom. Thus, dealer 1's prot can be expressed as at, = 3,,2oo,ooo[x1/(x1 + x2 + x3 + x4)] - 2,4oox1. The prot expressions for the other dealers are analogous. The partial spreadsheet that follows lists the prot ol 3 typial dealer (for various inventories) when it faces competitors with different average inventories. For instance, if dealer 1 stocks an inventory of 250 chars when the other dealers do likewise, then dealer 1's inventory' is 25 percent of the total. Thus, it sells exactly (251600) = zoo cars at a price of $4,000 each, while paying for 250 cars at $2,400 each. It: not prot is $200,000. a. Create a spreadsheet to complete the entries in the following payoff table. Hint: To compute cell G10, enter the formula: = momma/($310+ 3*G$5)-2.4*SBIO. Then simply copy this formula into the other cells of the table. (Adding dollar signs creates the appropriate absolute referenca to the dealers' inventory levels. For the row piayer's action, the sign always goes before the alphabetical coordinate, 31310. For the column player's action, it gou before the numerical reference, 535.) Also, in cells D7vD1o and E7, dealer 1 sells its entire inventory; thus, its payoffs are computed accordingly\". 1:. Find dealer 1's best inventory response to the various inventory actions of the other dealers. (Circle the greatest prot entry in each column of the table.) c. What is the equilibrium inventory level for each of the four dealers? d. If the dealers colluded to limit inventories, what wouldbe the maximum monopoly prot they could earn collectively? Would individual dealers have an incentive to cheat on their inventories? Explain. e. Mat would be the effect of free entry into the used-car business? 1 A B C D F. F G H I J K 2 USEDCARDEALERS 4 Dealer 1's Average Auto Inventory of the Other Three Dealers I 5 Inventory :75 I 200 I 225 I 250 I 275 300 I 325 I '7 I 175 - 280.0- 280.0 I 238.8 I 185.4 8 . 200 320.0 320.0 251.4 I 193.7 9 225 360.0 332.7 260.0 198.5 7 10 250 , 400.0 341.2 264.9 200.0 11 275 I I '12_ 300 13 _ 325 I4 _ 35 15