3) Fire Wings (F) and WingStop (W), the two places offering chicken-wings in Davis sell differentiated end-products, due to the different mix of spices they use. Further, Wingstop gets a higher demand as it is located closer to the Davis downtown. i) Quantity competition: Suppose they face inverse demands of pe = 112 - qw – 0.5qw and pw = 130 – qw – 0.52F respectively, where qr and qw are the number of buckets of wings produced by them everyday. (Do you see how Wingstop gets a higher demand?) Each firm has a marginal cost of m= 5 per unit. Solve for the Nash-Cournot equilibrium quantities. ii) Price Competition: For the same marginal cost as before, suppose Firm 1 faces a demand function of qr = 112 – 2pF + pw, and Firm 2 faces qw = 130 - 2pw +Pr. Solve for the Bertrand equilibrium.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)