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  • Print publication year: 2009
  • Online publication date: June 2012

2.4 - Input Profit Maximization

from PART II - THE THEORY OF THE FIRM

Summary

Most would agree that the excess of a college player's marginal revenue product over actual in-kind payment stays in the athletic department. But “talent collectors” also receive some of that value.

The Sports Economist Blog

Recall that the firm's backbone is the production function, shown in Figure 2.4.1.1.

Inputs, or factors of production, are used to make output, or product.

Market structure is an important element of the firm's optimization problem. The extremes are perfect competition and monopoly. A PC firm takes price as given and there is free entry, whereas a monopolist can choose P and enjoys a barrier to entry.

The Theory of the Firm is actually a group of three different optimization problems. Each one has its own interesting comparative statics analysis.

Input Cost Min: Choose inputs to minimize cost of a given output level

Key comparative statics: Cost function

Output Profit Max: Choose output to maximize profits

Key comparative statics: Supply curve

Input Profit Max: Choose inputs to maximize profit

Key comparative statics: Demand for an input

We have explored the first two optimization problems and seen how the cost function derived from the input cost minimization problem is used in the output side profit maximization problem.

Before we set up and find the initial solution for the input profit max problem, we need to discuss the market structure for each input. The firm has the same price-taking versus market power issue in hiring inputs.

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