A and B are Bertrand competitors selling two products, A and B. Demand for each product is: qA = 100 - 2PA + PB and qB = 100 - 4PB + PA a. Assume each firm has the same cost function Ci = 10qi. Derive (i.e., do not use formulae) and sketch the best response functions for these firms. (Put Alpha’s price on the vertical axis.) b. Solve for the equilibrium prices, quantities, and profits. (Solve for Alpha’s price first, to the nearest penny, and then find Beta’s price.) c. Now suppose that Alpha’s cost function changes to Ci = 30qi. Find the new best response functions, equilibrium prices, quantities and profits.
A and B are Bertrand competitors selling two products, A and B. Demand for each product is: qA = 100 - 2PA + PB and qB = 100 - 4PB + PA a. Assume each firm has the same cost function Ci = 10qi. Derive (i.e., do not use formulae) and sketch the best response functions for these firms. (Put Alpha’s price on the vertical axis.) b. Solve for the equilibrium prices, quantities, and profits. (Solve for Alpha’s price first, to the nearest penny, and then find Beta’s price.) c. Now suppose that Alpha’s cost function changes to Ci = 30qi. Find the new best response functions, equilibrium prices, quantities and profits.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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A and B are Bertrand competitors selling two products, A and B. Demand for each product is:
qA = 100 - 2PA + PB and qB = 100 - 4PB + PA
a. Assume each firm has the same cost function Ci = 10qi. Derive (i.e., do not use formulae) and sketch the best response functions for these firms. (Put Alpha’s price on the vertical axis.)
b. Solve for the
c. Now suppose that Alpha’s cost function changes to Ci = 30qi. Find the new best response functions, equilibrium prices, quantities and profits.
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