Derived demand is demand for resources (inputs) that is dependent on the demand for the outputs those resources can be used to produce. Inputs are demanded by a firm if, and only if, households demand the good or service produced by that firm.

The productivity of an input is the amount of output produced per unit of that input. Inputs can be complementary or substitutable. This means that a firm’s input demands are tightly linked together.

Faced with a capacity constraint in the short-run, a firm that decides to increase output will eventually encounter diminishing returns. Marginal product of labor (MP L ) is the additional output produced by one additional unit of labor.

The marginal revenue product (MRP) of a variable input is the additional revenue a firm earns by employing one additional unit of input, ceteris paribus. MRP L equals the price of output, P X, times the marginal product of labor, MP L.

When output price is constant, the behavior of MRP L depends only on the behavior of MP L. Under diminishing returns, both MP L and MRP L eventually decline. MRP L = P X  MP L

A competitive firm using only one variable factor of production will use that factor as long as its marginal revenue product exceeds its unit cost. If the firm uses only labor, then it will hire labor as long as MRP L is greater than the going wage, W*.

The hypothetical firm will demand 210 units of labor. W* =MRP L = 10

When a firm uses only one variable factor of production, that factor’s marginal revenue product curve is the firm’s demand curve for that factor in the short run.

Assuming that labor is the only variable input, if society values a good more than it costs firms to hire the workers to produce that good, the good will be produced. Firms weigh the value of outputs as reflected in output price against the value of inputs as reflected in marginal costs.

The two profit-maximizing conditions are simply two views of the same choice process.

Firms weigh the cost of labor as reflected in wage rates against the value of labor’s marginal product. Assume that labor is the only variable factor of production. Then, if society values a good more than it costs firms to hire the workers to produce that good, the good will be produced.

Land, labor, and capital are used together to produce outputs. When an expanding firm adds to its stock of capital, it raises the productivity of its labor, and vice versa. Each factor complements the other.

When P L = P K = $1, the labor-intensive method of producing output is less costly.

Two effects occur when the price of an input changes:  Factor substitution effect: The tendency of firms to substitute away from a factor whose price has risen and toward a factor whose price has fallen.  Output effect of a factor price increase (decrease): When a firm decreases (increases) its output in response to a factor price increase (decrease), this decreases (increases) its demand for all factors.

If labor markets are competitive, the wages in those markets are determined by the interaction of supply and demand. Firms will hire workers only as long as the value of their product exceeds the relevant market wage. This is true in all competitive labor markets.

Unlike labor and capital, the total supply of land is strictly fixed (perfectly inelastic).

The price of a good that is in fixed supply is demand determined. Because land is fixed in supply, its price is determined exclusively by what households and firms are willing to pay for it. The return to any factor of production in fixed supply is called pure rent.

The supply of land in a given use may not be perfectly inelastic or fixed. The supply of land of a given quality at a given location is truly fixed in supply.

A firm will pay for and use land as long as the revenue earned from selling the output produced on that land is sufficient to cover the price of the land. The firm will use land (A) up to the point at which: MRP A = P A

Profit-maximizing condition for the perfectly competitive firm is: where L is labor, K is capital, A is land (acres), X is output, and P X is the price of that output. P L = MRP L = (MP L X P X ) P K = MRP K = (MP K X P X ) P A = MRP A = (MP A X P X ) P L = MRP L = (MP L X P X ) P K = MRP K = (MP K X P X ) P A = MRP A = (MP A X P X )

Profit-maximizing condition for the perfectly competitive firm, written another way is: In words, the marginal product of the last dollar spent on labor must be equal to the marginal product of the last dollar spent on capital, which must be equal to the marginal product of the last dollar spent on land, and so forth.

If product demand increases, product price will rise and marginal revenue product will increase.

If the productivity of labor increases, both marginal product and marginal revenue product will increase.

The production and use of capital enhances the productivity of labor, and normally increases the demand for labor and drives up wages.

The Demand for Outputs right If product demand increases, product price will rise and marginal revenue product (factor demand) will increase—the MRP curve will shift to the right. left If product demand declines, product price will fall and marginal revenue product (factor demand) will decrease—the MRP curve will shift to the left. The Quantity of Complementary and Substitutable Inputs The production and use of capital enhances the productivity of labor and normally increases the demand for labor and drives up wages.

The Prices of Other Inputs When a firm has a choice among alternative technologies, the choice it makes depends to some extent on relative input prices. Technological Change The introduction of new methods of production or new products intended to increase the productivity of existing inputs or to raise marginal products.

marginal productivity theory of income distribution At equilibrium, all factors of production end up receiving rewards determined by their productivity as measured by marginal revenue product.