Suppose that there are only three manufacturing companies (Company A, Company B, and Company C) in a certain country that manufacture the same product with production levels xA, xB, and xC, respectively. It costs $xA2 for Company A to produce xA units of this product, whereas similar costs for Companies B and C are $xB2 and $xC2, respectively. If a total of x units of this product are produced by the three companies, consumers would be willing to pay $(M - x) for each unit, where M > x is a fixed number.
Describe whether you believe there is an opportunity for the companies to agree to particular production levels for each company so that their combined profits are maximized. What factor(s) do you believe to be influential in providing such an opportunity? What value do you recommend for the total production x?
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