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For Mathematically minded students, what is the alegbraic relationship between the equation for output and the equation for marginal product in exhibit 2 chapter 7?

For Mathematically minded students, what is the alegbraic relationship between the equation for output and the equation for marginal product in exhibit 2 chapter 7? Explain the circumstances under which the lon g run supply curve for an industry is a horizontal line. Next, explain the circumstances under which the long run supply curve for an industry is an upward sloping line.

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