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Two firms, DeSoto Cab (D) and Uber (U), sell taxi cab rides in San Francisco. Suppose...

Two firms, DeSoto Cab (D) and Uber (U), sell taxi cab rides in San Francisco. Suppose the demand curve for DeSoto is Dp = 60 - PD + 0.5pu while the demand curve for Uber is given by Du = 60 - Pu + 0.5pd. Suppose DeSoto has marginal cost of $25 and Uber has a marginal cost of $35. The two firms compete by choosing price (i.e. Bertrand competition).

(a) Derive each firm's best response (or reaction) functions.

(b) If Uber sets a price of $20, what price will DeSoto set and will it make any profits?

(c) Draw the demand curve for DeSoto if Uber sets a price of $20. Include its marginal revenue curve, marginal cost "curve," and the optimal price from part (b).

(d) What is the Bertrand-Nash equilibrium?

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Answer Desoto Cab: Dp = 60-10 +0.5Pu Uber Cab : Du = 60-Pu +0.500 MC, 125 MC = $35 (2) Now - profit (x) = TR-TC an [P-Mc D ToBeol Response function: Desoto Can : P = 85 +0.5 Pu Uber cab: Pu - 95 +0.5 PRO (b) of Pu- $20, then Pp - 85 +0.5x20 -85 +5 Po(0) TRO= Pox Dp (TR: Total Revenue) Dp = 60-80 +0.5Pu Op = 60-Po + 0.5X20 = 70 -Po Po=70-Dp TRO = Dp (To-Dp Marginal Revenue2. - MC - $25 0 2 2 ho t e Suantito. Dp to (d) Bertrand - Nosh (quelibolum: Prices where Best funcion interses each othen Bro& Pu= 95 +0.5 (58) » Pu = 47.5+ 14.5 - [Pu = 62] Therefore, Bertrand -Nash Equilibrium is Po= 58, Pu = 62]

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