The Labor Market For Athletic Talent

1
The Labor Market For Athletic Talent

• Economic Models of Labor Market
• Wage Differentials
• Impact of Market Restrictions
• Allocation of Talent

2
General Observations on theMarket for Athletic
Talent

• 1. Athletes at top of sports pyramid earn
  significant rents above their opportunity costs
• same as entertainers in music film
• wage differentials increase with skill
• people pay to see "the best"
• 2. Skills earnings peak early in life
• inter-temporal substitution
• train intensively ("play" becomes a job) retire
  early
• arms race in skills, fitness
• higher wages for select few increase competition

3
Supply Demand

• A. Supply
• B. Demand
• C. Equilibrium in Competitive Markets
• D. Wage Differentials

4
Supply CurvesIndividual Supply

• 2 opposing effects from increasing Wage Rate
• 1. substitution effect
• increase in wage makes leisure more costly
• incentive to work more
• incentive to shift timing of work high wage
  period
• 2. income effect
• permanent increase in wages raise wealth
• increases demand for leisure work less
• 1 2 slope of an individuals labor supply
  curve is generally ambiguous

5
Supply CurvesIndividual Supply (2)

• Consider typical person in U.S. economy over last
  century
• wage2000 gtgt wage1900
• hrs/wk2000 (35) ltlt hrs/wk1900 (65)
• Hence, supply curve of the individual in the U.S.
  is negatively sloped
• Reflects the income effect wealthier people
  consume more leisure (work less)

6
Supply CurvesIndividual Supply (2)

• Wage-induced substitution at individual level
• 1. Inter-temporal
• shift work to high wage periods (overtime)
• skilled occupations often require long hours
• work intensively while skills are earn a premium
• 2. Substitution between types of labor
• carpenter or mechanic?
• accountant or financial analyst?

7
Supply CurvesMarket Supply

• Market Supply relation btw wage rate and
  quantity of labor supplied to market
• 2 sources of market response to increase in W
• 1. change in hours by each individual (weak)
• 2. change in individuals supplying labor
• this can be very strong -gt S curve slopes up
• double wages of steel-workers in Ohio
• or small to non-existent -gt S curve is vertical
• double wages of brain surgeons in U.S.

8
Supply of Athletic Talent

• Some skills plentiful
• infielders that can't hit a major league curve
• S is horizontal at wage in alt occupation
• Other skills rare
• pitchers capable of ERA lt 4
• S turns vertical at limit
• Implications?
• need to bring in demand side of model

W
SP
SIF
Q
9
Labor DemandIndividual Firm Demand

• Firms hire labor when it is profitable
• compare benefits vs. costs
• hire if benefits exceed costs
• Benefit side
• incremental revenue from hiring labor
• Cost side
• wage and non-wage (taxes, benefits) costs

10
Firm Demand and MRP

• Benefits additional revenues from ?L
• Marginal Product of Labor MP ?Q/?L
• Marginal Revenue Product MRP
• MRP MRMP (?R/?Q)(?Q/?L) ?R/ ?L
• MRP will generally slope down
• diminishing returns -gt MP is negative function of
  L
• MR is either constant or decreasing in Q

11
Labor DemandIndividual Firm Demand (2)

• Costs
• direct costs are the wage rate per unit of L W
• non-wage hiring costs SS taxes, liability, etc
  H
• Profit Max Choice
• set L where MRP W
• or WH if H is non-zero
• Non-wage costs (Hgt0) reduce the firm's choice of
  labor from L to L

WH
W
MRP
L
L
12
Hiring Talent

• Think of Labor in terms of Talent or Skill
• Convenient in some applications to focus on value
  cost of a "talent" unit rather than an
  individual player
• players differ significantly in their talent
  levels
• a players wage is the wage per talent unit times
  her units
• Talent costs spread across players differently
• Champions can have a few superstars (Johnson
  Schilling Shaq Kobe) plus some everyday
  players, OR team that lacks superstars but is
  high quality across the board (2004 Pistons)

13
MRP of Athletic Talent

• MRP of Talent (or Skills)
• MR ?Rev/?Wins
• MP ?Wins/?Talent
• MRP MRMP ?Rev/?Talent

14
Market Demand

• Market Demand is the sum of the demand curves of
  all individual firms
• D S MRP
• Where S sums L over all firms in the market at
  each Wage
• Example
• let W10,
• let each firm i demand Li 20 at W 10
• Let there be 25 identical firms
• ? market demand is 500 at W 10 (20 per firm
  25 firms)
• repeat this summation for various wages and you
  have a market demand curve

15
Productivity Differences and Demand

• Rules Changes Demand
• A changes in league rules changes the
  productivity of different skills
• Football
• 1990 relaxed interpretation of holding by
  offensive line
• 1990 reduced contact allowed by DBs
• deliberately designed to increase passing "open
  up" game
• Result demand increased for WRs, decreased for
  RBs
• Baseball
• 1888 strikeout reduced to 3 strikes (scoring
  decreased)
• big swingers vs. contact hitters
• 1969 strike zone narrowed (scoring increased)
• hard throwers vs. control pitchers

16
Productivity Differences and Demand (2)

• Shaq vs. Vlade Divac
• best center in NBA vs. avg. center
• Shaq is more productive
• more rebounds, scoring, defense
• more "talent units"
• ? higher MRP for Shaq ? higher demand
• Demand for players w/ greater skills is higher
• Allocation of a single player
• Let MRP_shaq(LA) gt MRP_shaq(NY) gt MRP_shaq(DC)
  ...
• LA wins competitive bidding contest, ceteris
  paribus.
• Players go where their MRP is highest
• Big-money teams get the best players

17
Allocation of Talent in a League of
Profit-Maximizing Teams

• Let revenue-generating abilities of teams differ
• MRPB MRP in big city
• MRPS MRP in small city
• MRPB gtMRPS
• W is competitively determined wage
• Result profit max acquisition of talent implies
  that
• TB gt TS
• WTB gt WTS
• Big city teams acquire more talent have higher
  payroll
• "Competitive Imbalance"

W
WTS
WTB
MRPS
W
MRPB
TS
TB
Talent
18
Equilibrium in a Competitive Labor Market

• At Equilibrium W, L
• W MRP for all firms
• firms make profit-maximizing hires
• W supply price of workers (the opportunity cost
  at the margin)

SL
W
DL
L
19
Changes in Equilibrium Wages

• Demand Shifts
• Demand Increases w/
• Price of output
• Increase in productivity
• Demand Decreases w/
• Increase in non-wage costs

• Higher demand yields higher W, L

S
W2
W1
D2
D1
L1
L2
20
Changes in Equilibrium Wages (2)

• Supply Shifts
• Supply shifts back w/
• Higher opportunity costs
• Higher costs of skill acquisition
• ( vice versa)

• Less Supply raises W, lowers L

S2
S1
W2
W1
D
L1
L2
21
Equilibrium Wage Differentials

• Returns to Education
• D1 S1 supply demand for unskilled workers
• Educated workers acquire skills
• More productive (D2)
• Skills are costly to obtain (S2)
• W2/W1 measures the wage premium for educated
  workers
• Compensates for costs
• Rewards higher productivity
• Recent years W2/W1 is rising sharply. Why?

• Less Supply raises W, lowers L

S2
S1
W2
D2
W1
D1
22
Equilibrium Wage Differentials (2)

• The Gender Gap
• WF average female earnings
• WM average male earnings
• Gender Gap (newspaper version)
• original benchmark WF/WM .65
• Why?
• education, occupational choice, job tenure
• discrimination
• women now more educated, etc -gt WF/WM .75
• holding above 3 factors constant, WF/WM .95
• new battleground occupational segregation
  comparable worth "glass ceiling"

23
Exploitation in MLB The Reserve Clause

• Compare Competitive Monopsony Outcomes
• Theory
• Reserve System
• Yanks MRP for R. Clemens 10m
• Clemens' opp. cost 100k (as accountant)
• Yanks have exclusive rights to negotiate with
  Clemons
• W 100k
• Competitive Bidding
• Let Red Sox have MRP of 9.5m for Clemons
• Rangers MRP -- 9.1m
• Blue Jays MRP -- 8.7
• What is outcome of competitive bidding?
• W MRP (10m)
• big rents for Clemons relative to outside option
  (work as accountant)
• little rent relative to inside option (Red Sox)

24
Exploitation in MLB The Reserve Clause (2)

• Evidence
• Compare W to MRP competition gt W MRP
• Data exists on wages of players in reserve clause
  era
• Q What was MRP?
• A Ask Gerald Scully (Amer. Econ. Rev., 1974)
• Scully estimated MRP for pitchers batters
• W/MRP 0.15 on average
• wages were 15 of MRP!
• Enormous exploitation
• W far below what would obtain in competitive
  market

25
Scully's Model

• Team MR is a function of Winning Pct
• Player MP is contribution of Skill to Wins
• batters slugging percentage (SlugPct)
• pitchers strikeout to walk ratio (S/W)
• Estimated equations
• Revenue A 10,330 x WinPct (R2 .75)
• (t 6.6)
• MR of WinPct is 10,330 (in 1960s)
• WinPct A' .92 x SlugPct .90 x S/W (R2
  .88)
• (t4.4) (t5.9)
• Marginal Revenue Products
• MRP(B) 10,330 x .92 x team SlugPct
• MRP(P) 10,330 x .90 x team S/W

26
Scully's Conclusion

• Compare Team MRPs w/ Team Payrolls
• Batters' Salaries / MRP of Batters .15
• Pitchers' Salaries / MRP of Pitchers .15
• Players wages were approx. 15 of MRP!
• Conclusion Enormous exploitation relative to a
  competitive market standard
• Prediction Replacing reserve clause with free
  agency would increase W sharply

27
What Happened Next?

• 1975 arbitrator's decision in Messersmith/McNally
  case opened pandoras box, led to free agency
• Effect On Wages

28
Revenue Sharing's Impact on Equilibrium Wages

• Spring 2003 Labor Negotiations in MLB were hung
  up on magnitude of revenue sharing.
• Q Why would owners players be in such sharp
  disagreement over how much revenue owners would
  share among themselves?
• A higher shared revenues lead to lower wages
• Why? .......

29
Revenue Sharing's Impact on Equilibrium Wages (2)

• Compare competitive wages w/ w/o sharing
• Earlier example, Roger Clemens' W 10m
• Now suppose 50 of revenue is shared.
• Yank's net MRP after revenues sharing
• 10m(0.5) 10m(0.5)(1/N)
• with N 30, Yankees Net MRP falls to 5.167m
• Result Clemens' W falls to 5.167m
• NFL has greatest extent of shared revenue and
  consequently biggest gap between W MRP of major
  pro leagues.
• Revenue sharing is not player-friendly, hence
  their unions fight against it.