Midterm #1

More documents

Recommendations

Info

. Solve the Bertrand game with differentiated products. Make sure you solve for the market price.[Hint: use the direct demand function]Levis maximizes the following profit functionHence the first order condition with respect tois:Solving for, we obtain Levi’s best response function:(I)And by symmetry, True Religion’s best response function is:(II)Substituting (II) into (I),By symmetry,c. Which market structure, a Cournot or a Bertrand, would yield a higher market price? How wouldchanging the degree of product differentiation affect the relative difference between the twomarket-structure outcomes?P C =4.45>4.30=P B , hence Cournot yields a higher market price. The more differentiated the products are,the smaller the difference between the Cournot and Bertrand prices.
Question #2 [25 Points]In Ben Barber there are two suppliers of distilled water, labeled firm A and firm B. Distilled water isconsidered to be a homogenous good. Let p denote the price per gallon, q A quantity sold by firm A, andq B the quantity sold by firm B. Firm A and firm B bear unit production costs of c A = $20 and c B = $100 perone gallon of water, respectively. That is, firm A is more efficient than firm B. Ann Barber's inversedemand function for distilled water is given byp = 140- 2Q = 140 - 2(q A + q B )where Q = q A + q B denotes the aggregate industry supply of distilled water in Ben Barber.a. Assuming that the firms compete in prices p A and p B , write down each firm's price best responsefunction, and solve for the price each firm sets in a Bertrand-Nash equilibrium. [Hint: the bestresponse function must also consider the monopoly price]A's monopoly price can be found by solving MR = 140- q m A = c A = 20 yielding q m A = 30 and hence p m A =$80.B's monopoly price can be found by solving MR = 140 - q m B = c B = 100 yielding q m B = 10 and hence p m B =$120.Hence, the firms’ best-response functions are:Therefore, the unique Nash-Bertrand equilibrium is pbA = $80 and pbB = $100. The corresponding profitlevels are ∏ A = (80 - 20)30 = $1800 and ∏ B = 0.b. Suppose that firm B invests in R&D and manages to reduce its unit production cost to c B = $60.Firm A's unit cost stays the same, c A = $20. Consider a sequential quantity game in which firm Bsets its output level q B before firm A sets q A . Compute the Stackelberg equilibrium output andprofit levels of the two firms.In stage II, firm A solvesIn stage I, firm B solves,Thus, q A = 25, Q = 35, p = $70, so∏ A = (70 -20)25 = $1250 and ∏ B = (70 - 60)10 = $100:
Page 1: Name:_______________________Midterm

Midterm #1

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?