Consider an industry comprised of three identical firms faced with a linear cost function given by:...

 

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Consider an industry comprised of three identical firms faced with a linear cost function given by: C(qi) = cqi, for i=1,2,3. Let inverse market demand be given by: where Qq1 +92 +93. P(Q) = a - bQ, 1. Compute the Cournot equilibrium; that is, find prices, quantities, and profits. 2. Suppose that firms 1 and 2 merge, converting the market into a duopoly consisting of the "superfirm" and firm 3. Compute the new Cournot equilibrium. Once again find prices, quantities, and profits. 3. Suppose that all three firms merge. Compute quantities, prices, and profits for the cartel solution. 4. Suppose that firm 1 and 2 represent two members of OPEC - Saudi Arabia and Venezuela, say while firm 3 is a non-OPEC oil exporting country - Russia, say. Describe the dynamics of OPEC. (Hint: You can re-interpret the solution to part 2, as 1 firm deviating from the fully cartelized solution. Is it convenient to have a partial cartel?) Consider an industry comprised of three identical firms faced with a linear cost function given by: C(qi) = cqi, for i=1,2,3. Let inverse market demand be given by: where Qq1 +92 +93. P(Q) = a - bQ, 1. Compute the Cournot equilibrium; that is, find prices, quantities, and profits. 2. Suppose that firms 1 and 2 merge, converting the market into a duopoly consisting of the "superfirm" and firm 3. Compute the new Cournot equilibrium. Once again find prices, quantities, and profits. 3. Suppose that all three firms merge. Compute quantities, prices, and profits for the cartel solution. 4. Suppose that firm 1 and 2 represent two members of OPEC - Saudi Arabia and Venezuela, say while firm 3 is a non-OPEC oil exporting country - Russia, say. Describe the dynamics of OPEC. (Hint: You can re-interpret the solution to part 2, as 1 firm deviating from the fully cartelized solution. Is it convenient to have a partial cartel?)