Suppose there are exactly two farms, Farm A and Farm B, producing buffalo gourds in our...

Suppose there are exactly two farms, Farm A and Farm B, producing buffalo gourds in our market. They face a common inverse demand curve, P = 60 – (QA + QB), where QA and QB are the number of gourds produced by each farm. (Note that the gourds grown on the two farms are perfect substitutes.) Each farm faces marginal cost = average cost = $6 per gourd. a. Suppose these farms compete by choosing their profit maximizing level of output, conditional on the other firm’s choice of a level of output (so they are playing “Cournot” strategies).

Derive QA(the profit maximizing choice for A) as a function of QB. That is, find the QA that equates marginal revenue and marginal cost.

To do this, note that Total Revenue for A = PQA = (60-(QA + QB)) * QA, which means that Marginal revenue for A = 60 - 2QA - QB

Also write down the profit maximizing value of QB as a function of QA. Substitute one profit- maximizing function into the other to derive the resulting levels of QA, QB, and P. Describe why this result is a Nash equilibrium.

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Expert Solution

Rahul Sunny answered 2 years ago

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