Factor Demands for Profit-Maximizing Firms

What determines the demand for any factor of production? We can answer this question by analyzing how a profit-oriented firm chooses its optimal combination of inputs.

Imagine that you are a profit-maximizing farmer. In your area, you can hire all the farmhands )’OU want at S20,000 per worker. Your accountant hands you a spreadsheet with the data in Table 12-3.How would you proceed? .

You could try out different possibilities. If you hire one worker, the additional revenue (the MRP)is $60,000 while the ‘marginal cost of the worker is ~O,()()(), so your extra profit is’ $40,000. A second worker gives you an MRPof$30,OOO for an additional profit of $10,000. The third worker produces extra output yielding revenue of only $15,000 but costs $20,000; hence, it is not profitable to hire the third worker. Table 12-3 shows that the maximum profit is ‘earned by hiring two workers.

By using this reasoning, we can derive the rule for choosing the optimal combination of inputs: To maximize profits, firms should add inputs up to the point where the marginal revenue product of the input equals the marginal cost or price, of the input.’ ‘ For perfectly competitive factor markets, the rule is even simpler. Recall that under perfect competition the marginal revenue product equals price times marginal product (MRP =’p X MP).

We can understand this rule by the following Say that each kind of input is bundled Into little packages each worth $I-packages of$I worth of labor, $1 worth of land, and so forth. To maximize profits, firms will purchase inputs up to that point where each little $1 package produces output which is worth just $1. In other words, each $1 input package will produce NIP units of corn so that the MP X P just equals $1. of the $1 units is then exactly $1 under profit maximization.

Suppose that you own a cable’ television.monopoly in Denver. If you want to maximize profits, you will want to choose the best combination of workers, land easements for your cables, trucks, arid testing equipment to minimize costs. If a month’s truck rental costs $8000′ while’ monthly labor costs per worker are $800, costs are minimized when the marginal products per dollar oj input are the same. Since , trucks cost 10 times as much as labor; truck MPmust be 10 times labor’MP. ‘ Least-cost rule: Costs are minimized when the marginal product per dollar ofinput is equalized for each input. This holds for both perfect and imperfect’competitors in product markets.

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