• Recall: firms convert some goods to other goods:

• Inputs: x1,x2,⋯,xn

  • Examples: worker efforts, warehouse space, electricity, loans, gasoline, cardboard, fertilizer, computers, software programs, etc

• Output:¹ q

  • Examples: oil, cars, legal services, mobile apps, vegetables, consulting advice, financial reports, etc

• Suppose a firm sells output q at a price p

• It can buy each input xi at an associated price pi

  • labor l at wage rate w
  • capital k at rental rate r

• Profit ⟹ improving the (total) value of resources

  • bought inputs at some total cost
  • sold as final product at some market price

• The price of a factor is governed by the same market forces as output: Supply and Demand

• Supply of Factor: willingness of factor owners to accept and sell/rent their services to firms

  • landowners, workers, capitalists, resource owners, suppliers

• Demand for Factor: willingness of firms to pay for factor services

• In functioning factor markets, the factor price represents the opportunity cost of hiring a factor for an alternative use

  • Firms not only pay for direct use of a factor, but also indirectly for not using it in an alternate process!

• Example: a producer of hammers buys steel, pays (the opportunity cost) for "taking" the steel away from alternative uses

• Example: e.g. salary for a skilled worker must be high enough to keep them at their current firm, and not be attracted to other firms/industries

• Empirically, about 70% of total cost of production comes from labor

• We'll focus just on the market for labor as an example factor market

• Can do the same for any factor market

  • (e.g. capital, land, materials, etc.)

MRPL=MPL∗MR(q)

• For a firm in a competitive (output) market, firm's MR(q)=p, hence

MRPL=MPL∗p

where p is the price of the firm's output

• Marginal benefit of hiring labor, MRPL falls with more labor used

  • production exhibits diminishing marginal returns to labor

• Choke price for labor demand: price too high for firm to purchase any labor

• We've seen a falling MRPL, the marginal benefit of hiring labor

• Marginal cost of hiring labor, w, remains constant

  • so long as firm is not a big purchaser in the factor market

• At low amounts of labor, marginal benefit (MRPL)<w marginal cost

• Firm will hire more labor

• At high amounts of labor, marginal benefit (MRPL)<w marginal cost

• Firm will hire less labor

• Firm hires L∗ optimal amount of labor where w=MRPL (MB=MC)

• Equivalently (rearranging): MR=wMPL

  • implies that firm's producing the profit-maximizing output q∗ means firm is using the optimal amount of labor L∗

• Recall supply is the minimum willingness to accept, the minimum price necessary to bring a resource to market

• But all (equivalent) labor is paid the market wage, w∗ determined by market labor supply and labor demand

• Some workers would have accepted a job for less than w∗

• Labor earns economic rent in excess of what is needed to bring it into the market (its opportunity cost)

• Consider a factor (such as land) for which the supply is perfectly inelastic (e.g. a fixed supply)

• Then the entire value of the land is economic rent!

• The less elastic the supply of a factor, the more economic rent it generates!