Find the output-reaction equations for both firms

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Reference no: EM131171029

Mathematical Oligopoly Problem. Suppose a duopoly is operating using the following information. The firms are denoted Firm a and Firm b.

Demand: P = $1,250 – Q

Q = Qa + Qb, (this is stating that the market quantity is the sum of the two firm’s quantities)

TRa (Total Revenue for Firm a) = $1,250Qa – Qa2 – Qa*Qb

MRa (Marginal Revenue for Firm a) = $1,250 – 2Qa – Qb MCa (Marginal Cost for Firm a) = MCb (Marginal Cost for Firm b) = $50

Fixed Costs = $0, for both firms.

a. Use the Cournot solution method to find the output-reaction equations for both firms

b. Use the Cournot solution method to find Qa*, Qb*, Q*, P*

c. Suppose now that Firm a is the Stackelberg leader. Suppose further that when Firm a has prior knowledge about Firm b’s reaction curve, they now have an MRa = $650 – $1Qa. Use the Stackelberg solution method to find Qa*, Qb*, Q*, P*.

d. Assume the products sold by these firms are identical. Use the Bertrand model for identical p6roducts to solve for P* and Q*.

e. Compare/contrast the findings from parts 16b, 16c, and 16d. Explain any differences.

Reference no: EM131171029

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