Chapter 19: Problem 714

It is clear from the definition of profit why a monopolist would maximize profit at the point where the difference between Total Revenue and Total Cost is greatest. Yet it is not intuitively clear why this is necessarily the same point where Marginal Revenue = Marginal Cost. Explain why the first rule of profit maximization (Maximize \(\mathrm{TR}-\mathrm{TC}\) ) is equivalent to the second rule of profit maximization \((\mathrm{MC}=\mathrm{MR})\).

Short Answer

Expert verified

Maximizing profit at the point where the difference between Total Revenue (TR) and Total Cost (TC) is greatest is equivalent to the point where Marginal Revenue (MR) equals Marginal Cost (MC) because when we take the derivative of the profit function (TR-TC) with respect to quantity and set it equal to 0, we obtain the equation MR - MC = 0, which leads to MR = MC. Therefore, both rules of profit maximization are mathematically equivalent.

Step by step solution

Understand the Concepts

- Total Revenue (TR) is the total amount of money a firm receives from selling a product or service. It can be calculated as price of the product multiplied by the quantity sold. - Total Cost (TC) is the total cost incurred to produce a specific number of products, including both fixed and variable costs. - Marginal Revenue (MR) is the additional revenue generated from selling one more unit of a product. - Marginal Cost (MC) is the additional cost incurred from producing one more unit of a product.

Express Profit

To maximize profit, a monopolist wants to find the point where the difference between Total Revenue and Total Cost is the largest. Mathematically, that means: Profit = TR - TC To maximize Profit, we must find the maximum point of this function.

Find the Derivative of Profit

To find the maximum point of the Profit function, we can take the derivative of Profit with respect to quantity (q) and set it equal to 0, to find the critical points. \(\frac{d}{dq}(\mathrm{TR} - \mathrm{TC}) = \mathrm{MR} - \mathrm{MC} = 0\)

Equate Marginal Revenue and Marginal Cost

Since we already took the derivative and set it to 0, we obtain this formula: \(\mathrm{MR} - \mathrm{MC} = 0\) Hence, \(\mathrm{MR} = \mathrm{MC}\)

Conclusion

From the above steps, it is clear that maximizing the profit function (TR-TC) is mathematically equivalent to finding the point where Marginal Revenue equals Marginal Cost (MR = MC). Therefore, the first rule of profit maximization (maximizing TR-TC) is equivalent to the second rule of profit maximization (MC = MR).

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