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8. Stackelberg model with entry deterrence In Pasturetown, only Darnell and Eleanor can raise free-range chickens on their farms. Assume that Darnell and Eleanor can collect and sell a large quantity of eggs at no cost and that free-range eggs sold outside Pasturetown cannot be transported into the town for sale Suppose that, in this market, Darnell decides how many eggs per day he is going to sell, and then Eleanor makes her decision after observing Darnell's quantity choice. The market demand for eggs is given by Q - 20 - P. Based on this demand, Darnell's and Eleanor's best-response functions are given on the following graph. Dame I's BRF 20 ELEANOR'S QUANT ITY (Gross of eggs per day) Stackelberg Equilibrium Liz Point 2 Eleanor's BRF 10 12 14 16 18 DARNELL'S QUANTITY (Gross of eggs per day) Complete the first row of the following table by indicating the total production, market price, and profits for Darnell and Eleanor when Darnell chooses the Stackelberg equilibrium quantity. Now suppose Darnell wants to deter Eleanor from entering the market by forcing her to sell an output level that would not be profitable. Complete the second row of the table with the values that would result if Darnell were to sell 12 gross of eggs (Point 2) and Eleanor still enters the market, and the third row of the table with the values that would result if Eleanor does not enter the market. Total Production Market Price Darnell's Revenue Eleanor's Revenue (Gross per day) (Dollars per gross) ( Dollars) (Dollars Stackelberg equilibrium Point 2 (entry) Point 2 (no entry)Now suppose Darnell wants to deter Eleanor from entering the market by forcing her to sell an output level that would not be profitable. Complete the second row of the previous cable with the values that would result if Darnell were to sell 12 gross of eggs (Point 2) and Eleanor still enters the market, and the third row of the table with the values that would result if Eleanor does not enter the market. If there were a fixed cost of production equal to $17, then Eleanor would earn a profit of from entering the market at Point 2. Given that she be deterred from entering if Damell produces at Point 2, Darnell maximizes his own profits by producing atNow suppose Darnell wants to deter Eleanor from entering second row of the previous table with the values that wou and will not tow of the table with the values that would r will If th fixed cost of production equal to $17, then she be deterred from entering if Darell pro$25 $16 market by forcing her to s Itout level that would not be profitable. Co ult if Darnell were to sell -$1 of eggs (Point 2) and Eleanor still enters f Eleanor does not enter ker. $1 or would earn a profit of rom entering the market at Point 2. G at Point 2, Darnell maximizes his own profits by producing atsecond row of the previous table with the values the and the third row of the table with the valves that w the Stackelberg equilibrium bduction equal to $17 Point 2 rom entering if Dam
