Profit Maximization and Labor Demand

1
Profit Maximization and Labor Demand

• Fundamental assumption Firms seek to maximize
  profits.
• Firms 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.

2
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
  workers MRP and Wage.

3
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?

4
Adjusting your labor force

• If W MRP What action should the firm take?
• If W
• The firm will maximize profits with respect to
  the hiring of workers when W MRP

5
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 workers
  marginal revenue product.
• A monopsony, though, is the sole buyer in the
  market. Consequently the monopsonist can require
  workers to accept wages below the workers
  marginal revenue product.

6
EXPLOITATION

• 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.

7
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.

8
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.

9
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.

10
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.

11
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 Players
  Labor Market. Journal of Political Economy,
  (June) 242-258.

12
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.

13
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.

14
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).

15
Problem with FOA?

• Only the supply side is considered. Arbitrators
  compare a players 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.

16
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.

17
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
  baseballs 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.

18
Measuring Marginal Revenue Product

• Scully, Gerald W. 1974. Pay and Performance in
  Major League Baseball. American Economic Review,
  64, No. 6917-930.
• 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. Whats Wrong with
  Scully-Estimates of a Players 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.