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Profit Maximization and Labor Demand Fundamental assumption: Firms seek to maximize profits. Firm’s maximize profits be equating marginal revenue and marginal cost. With respect to inputs, firms will add inputs as long as the income generated by the input exceeds the expense of the input.

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profit maximization and labor demand
Profit Maximization and Labor Demand
  • Fundamental assumption: Firms seek to maximize profits.
  • Firm’s maximize profits be equating marginal revenue and marginal cost.
  • With respect to inputs, firms will add inputs as long as the income generated by the input exceeds the expense of the input.
  • A firm will stop hiring inputs when the income an additional worker produces equals the expense of hiring the worker.
marginal revenue product
Marginal Revenue Product
  • How do we measure the marginal income from an additional input?
  • The value of a worker can be divided into two parts:
    • Marginal Product of Labor: the productivity of the last unit of labor hired (i.e. the productivity of a worker).
    • Marginal Revenue of Output: the revenue generated by the last unit sold (i.e. the value of a unit produced).
    • Marginal Revenue Product = MP * MR
  • How do we measure the marginal expense of an additional input?
  • In a perfectly competitive labor market, the marginal expense of labor is the wage.
  • To maximize profits, the firm will equate the worker’s MRP and Wage.
the law of diminishing returns and profit maximizing hiring
The Law of Diminishing Returns and Profit Maximizing Hiring
  • The Law of Diminishing Returns – As you, hire more workers, holding all else constant, the amount of output from each additional worker you add will eventually decline.
  • Implications: As a firm expands the size of its labor force, the productivity of each additional worker declines. In other words, marginal product (and MRP) decline as the number of workers increases.
  • If wages are set by the market, how many workers should the firm hire?
adjusting your labor force
Adjusting your labor force
  • If W > MRP What action should the firm take?
  • If W < MRP What action should the firm take?
  • The firm will maximize profits with respect to the hiring of workers when W = MRP
a monopsony
A Monopsony
  • Monopsony – a single buyer in a market.
    • Contrast with a monopoly.
  • A firm in a competitive labor market is forced to pay a worker a wage equal to the worker’s marginal revenue product.
  • A monopsony, though, is the sole buyer in the market. Consequently the monopsonist can require workers to accept wages below the worker’s marginal revenue product.
  • Implication: Monopsonistic firms exploit their workers.
  • Joan Robinson (1933): “What is actually meant by exploitation is usually that the wage is less than the marginal revenue product.”
early baseball history
Early Baseball History
  • The National Association of Professional Base Ball Players (organized 1871) established a rule that you could not sign a player from another team during the regular season. Players were free to sign with anyone in the off-season.
  • The rule prohibiting in-season signings was broke by William Hulburt, owner of the Chicago team (who raided the championship Boston team during the 1875 season) and the National League of Professional Baseball Clubs was formed in 1876.
  • William Hulbert is the one who initially proposes the reserve clause.
the reserve clause
The Reserve Clause
  • “If, prior to March 1,.... the player and the club have not agreed upon the terms of such contract [for the next playing season], then on or before ten days after said March 1, the club shall have the right to renew this contract for the period of one year on the same terms except that the amount payable to the player shall be such as the club shall fix in said notice.”
imposing the reserve clause
Imposing the Reserve Clause
  • The Reserve Clause - A renewal clause in each uniform player contract, which permits the team to renew the contract for the following year at a price the team may fix.
  •  In 1878, players could not be signed to a new team until after the season ended.
  • In 1879, a limited reserve clause (applicable to five players) was enacted.
  • In 1889 it was applied to all players.
  • After the courts ruled that this clause was unenforceable (due to its vagueness), the clause was revised until it achieved the form reported.
interpreting the reserve clause
Interpreting the Reserve Clause
  • The teams argued that the new one year contract contained the clause. Even if the player and team did not agree to terms, the new one year contract still contained the clause. Hence a player was effectively bound to a team for life.
  • Some form of a reserve clause has been employed in each of the four major North American sports.
the theoretical impact of the reserve clause
The Theoretical Impact of the Reserve Clause
  • To understand the impact of the reserve clause we turn to the work of Simon Rottenberg.
  • Rottenberg, Simon. 1956. “The Baseball Player’s Labor Market.” Journal of Political Economy, (June): 242-258.
additional features of labor markets in sports
Additional Features of Labor Markets in Sports
  • Free Agency
  • Final Offer Arbitration
  • Payroll Caps
  • The Draft
  • Each of these will be introduced in chapter eight. In our discussion of labor unions (chapter nine) we will offer further details regarding the origins of these institutions.
free agency
Free Agency
  • Free Agency – The right for a player to offer his or her services to the highest bidder.
  • Starting in the 1970s, free agency was implemented in each of the four major North American Sports.
    • MLB: After six seasons
    • NBA: After the 1999 CBA, after five seasons.
    • NFL: After four seasons
    • NHL: After four seasons
  • In the NBA, NHL and the NFL free agency is obtained in stages, with players first being made restricted free agents.
final offer arbitration
Final Offer Arbitration
  • Final Offer Arbitration – if a player and a team cannot agree to a contract, each side submits its final offer to an independent arbitration panel that selects on final offer or the other.
  • Note: No compromise is allowed.
  • What is the advantage of FOA? By choosing one offer or the other, the sides are forced to be more reasonable (relative to a ‘split the difference’ approach).
problem with foa
Problem with FOA?
  • Only the supply side is considered. Arbitrators compare a player’s wage to the wages of players with a similar level of productivity. What if these wages were chosen incorrectly? Because FOA does not consider the demand side of the market, these mistakes are repeated.
payroll caps and the draft
Payroll Caps and the Draft
  • Payroll Caps (Salary Caps) – a maximum payroll figure for each team.
  • The NBA Payroll Cap is a ‘soft’ cap due to the Larry Bird Exception.
  • Note: The 1999 Collective Bargaining Agreement did introduce the first salary cap.
  • The NFL Payroll Cap is a ‘hard’ cap. Because NFL salaries are not guaranteed, every player (except those with large signing bonuses) is playing for his job.
the draft
The Draft
  • The Reverse-Order Draft
    • Initially amateur athletes could negotiate with every team. Hence there was a free market for unsigned players.
    • The monopsony power of professional leagues was eventually extended to eliminate this loophole.
    • The first draft was introduced by the NFL in the 1930s.
    • Baseball did not introduce its draft until 1964. Foreign born players are still not selected in baseball’s draft.
  • Does the monopsony power of professional sports leagues lead to the exploitation of players? The answer to this question requires that we measure the marginal revenue product of professional athletes.
measuring marginal revenue product
Measuring Marginal Revenue Product
  • Scully, Gerald W. 1974. “Pay and Performance in Major League Baseball.” American Economic Review, 64, No. 6:917-930.
  • Blass, Asher A. 1992. “Does the Baseball Labor Market Contradict the Human Capital Model of Investment?” The Review of Economics and Statistics, 74, No. 2: 261-268.
  • Krautman, Anthony. 1999. “What’s Wrong with Scully-Estimates of a Player’s Marginal Revenue Product.” Economic Inquiry, 37, No. 2; April: 369-381.
  • Berri, David J. “A Simple Model of Worker Productivity in the National Basketball Association.”