Input Demand: Labor and Land Markets

Demand for Inputs: A Derived Demand 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  this means that firms will layoff employees when the demand for its product falls and will hire fewer workers when the price of labor (wages) increases.

Inputs: Complementary and Substitutable The productivity of an input is the amount of output produced per unit of that input. Labor Productivity: Q/L (output per hour of labor) Inputs can be complementary or substitutable. This means that a firm’s input demands are tightly linked together. Complements: as the firm hires more workers, it will need to employ more machinery (computers, etc.) for labor to use. Substitutes: as labor becomes more costly firms will automate by buying machinery that can do what labor does.

Marginal Product and Marginal Revenue Product Faced with a capacity constraint in the short-run, a firm that decides to increase output will eventually encounter diminishing marginal product. Marginal product of labor (MPL) is the additional output produced by one additional unit of labor. Marginal Revenue Product of Labor (MRPL) is the additional revenue a firm earns by employing one additional unit of labor, holding all else constant. Suppose Px is the price of output  MRPL = Px * MPL

Marginal Revenue Product Per Hour of Labor in Sandwich Production (One Grill) (1) TOTAL LABOR UNITS (EMPLOYEES) (2) TOTAL PRODUCT (SANDWICHES PER HOUR) (3) MARGINAL PRODUCT OF LABOR (MPL) (SANDWICHES PER HOUR) (4) PRICE (PX) (VALUE ADDED PER SANDWICH)a (5) MARGINAL REVENUE PRODUCT (MPL X PX) (PER HOUR) - 1 10 $ .50 5.00 2 25 15 7.50 3 35 4 40 5 2.50 42 1.00 6 aThe “price” is essentially profit per sandwich; see discussion in text.

Marginal Revenue Product Per Hour of Labor in Sandwich Production (One Grill) MRPL = Px*MPL When output price is constant, the behavior of MRPL depends only on the behavior of MPL. Under diminishing returns, both MPL and MRPL eventually decline.

Determining the Profit-Max Level of Labor: What is the Firms’ Demand for Labor? 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 MRPL is greater than the going wage, W*. Suppose W = $2.50 

In General Labor Market Representative Firm S W D MRPL L* labor Labor 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. Profit-max rule: hire L* where MRPL = W

Comparing Marginal Revenue and Marginal Cost to Maximize Profits We have 2 profit-maximizing rules: The output rule: choose q* where MR = MC The input rule: choose L* where MRPL = W These two rules should be consistent: the L* from the input rule should be capable of producing the q* units from the output rule. 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 The two profit-maximizing conditions are simply two views of the same choice process. If the only variable factor of production is labor, the condition W* = MRPL is the same condition as P = MC. The two statements are exactly the same thing.

Many Labor Markets 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. Examples:

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

Demand Determined Price 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.

Land in a Given Use Versus Land of a Given Quality 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.

Rent and the Value of Output Produced on Land 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: MRPA = PA Where MRPA is defined as Px*MPA

The Firm’s Profit-Maximization Condition in Input Markets Profit-maximizing conditions for the perfectly competitive firm with 3 types of variable inputs: are PL = MRPL = Px*MPL PA = MRPA = Px*MPA PK = MRPK = Px*MPK where L is labor, K is capital, A is land (acres), X is output, and PX is the price of that output.

The Firm’s Profit-Maximization Condition in Input Markets 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.

Input Demand Curves MRPL=PX*MPL If product demand increases (Px ), product price will rise and marginal revenue product will increase  The Firm’s demand for inputs increases.

Input Demand Curves MRPL=PX*MPL If the productivity of labor increases (due to more, better machinery/computers), marginal product increases causing marginal revenue product will increase  The firm’s demand for labor will increase.

Impact of Technological Change Technological change refers to the introduction of new methods of production or new products intended to increase the productivity of existing inputs or to raise marginal products. Technological change can, and does, have a powerful influence on factor demands. When we aggregate up all the firms’ higher demand curves for labor, we see the entire demand curve for labor shift right, pushing up wages.