Maximizing Profit: Understanding the Optimal Output Rule for Price-Taking Firms in Social Science

price-taking firm’s optimal output rule

a price-taking firm’s profit is maximized by producing the quantity of output at which the market price is equal to the marginal cost of the last unit produced.

The optimal output rule for a price-taking firm is to choose the level of output where the firm’s marginal revenue (MR) is equal to its marginal cost (MC). In other words, the firm will maximize profit by producing the quantity of output where the additional revenue gained by producing an additional unit of output is equal to the additional cost incurred.

Mathematically, the optimal output rule can be expressed as follows:
MR = MC

In the short run, where some inputs are fixed and others are variable, the optimal output level will occur where the marginal cost of production equals the marginal revenue received for that level of output. This will be the level of output where the firm earns the highest possible profit.

In the long run, all inputs are assumed to be variable, and the firm can adjust its production capacity as well as output level. In the long run, the optimal output level occurs where the marginal cost of production equals the average revenue received for that level of output. This will be the level of output where the firm earns normal profit.

Therefore, a price-taking firm will produce the quantity of output where marginal revenue equals marginal cost in the short run, and where average revenue equals marginal cost in the long run. By doing so, the firm can achieve its profit-maximizing output level.

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