Variable Pay Contd

1
Chapter 10

• Variable Pay (Contd)

2
Piece Rates Two effects

• 2. Provides incentive to work harder
• Talk about this today

• 1. Composition Screen out less productive
  workers

2/unit
/hr
10/hr
5/hr
Choose piece rate
Choose hourly pay
3
Reading for Next Class

• http//www.businessweek.com/magazine/content/07_46
  /b4058065.htm

4
Question 1

• You pay workers 10/unit to sell MP3 players.
  They work 30 hrs/wk and sell 300 units
• You raise that to 11 and find that they work 35
  hours week and sell 350
• If you raise the piece rate to 12/unit, your
  workers will likely work
• A. lt40 hrs/wk
• B. 40 hrs/wk
• C. gt40 hrs/wk

5
Eliciting Effort

• Increasing marginal disutility of effort
• For piece rates or commissions, pay is in terms
  of of Net Revenue
• Net Rev (Total Rev Non-labor Costs)
• This is how much worker nets for you, before you
  pay him(her).
• Pay higher Net Rev? increased effort.
• Diminishing return

/wk
90/unit
30/unit
hrs
6
Net Revenue

• MP3 players cost 10 to make. They sell for 100.
  A worker sells 20/wk. What is the workers net
  revenue?
• A. 2000/wk
• B. 1000/wk
• C. 1800/wk
• D. Cant tell
• Net revenue is 90/unit, If worker is paid
  30/unit this is same as 33 of Net Revenue

7
Question

• In theory, what rate of commissions should you
  pay to maximize profit (i.e., what share of net
  revenues?)
• A. 0
• B. 10
• C. 100
• D. 200
• E. It depends

8
Proof of Optimal Commission Rate

• Part 1 Worker decision Effort
• Cost of Effort Let C(E)E2
• 1 additional unit of effort E yields 1 unit of
  output
• Worker pay is aßE.
• Worker maximizes benefits costs
• MAXE (aßE)-C(E)
• FOC ß-C(E)0
• C(E) ß
• Slope effort curve Slope compensation line

C(E)
Different piece rates (aßE)
E
9
Proof of Optimal Commission Rate

• Part 1 Worker decision Effort
• Cost of Effort Let C(E)E2
• 1 additional unit of effort E yields 1 unit of
  output
• Worker pay is aßE.
• Worker maximizes benefits costs
• MAXE (aßE)-C(E)
• FOC ß-C(E)0
• C(E) ß
• Slope effort curve Slope compensation line

• Effort Supply Curve
• Where is workers E below?

C(E)
(aßE)
A
C
B
E
10
Proof of Optimal Commission Rate

• Part 2 Firm Decision
• Firm must get worker to work
• Need paygteffort cost aßEgtC(E)
• aßEC(E) minimizes cost
• Now profit max
• MAXß,a E-( a ßE)
• MAXß,a E-C(E)
• F.O.C (1-C(E))(dE/d ß)0
• C(E)1. Gives us E
• But we know C(E) ß from previous slide. So ß
  1.
• Slope of effort curve slope of Net rev line 1

• Firm maximizes profit by finding maximum distance
  between Net Rev and Cost.

C(E)
Net Rev Slope 1
Slope 1
E
E
11
Proof of Optimal Commission Rate

• Firm Decision (Contd)
• ß 1.
• Need to find a
• We know a ßEC(E)(Firm pays minimum needed
  to get effort)
• a EC(E)
• aC(E)-E
• a is negative!

C(E)
Net Rev Slope 1
E
E
A
a
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Interpretation

• ß 1
• Pay workers 100 of what they earn in net
  revenues
• a negative
• Charge workers a to work for you.
• Given the compensation line (in red), where does
  worker choose to work?
• Answer E.
• This is only point on red line that gets
  compensation to equal effort cost
• Worker paid just enough to be willing to stay.

C(E)
Net Rev Slope 1
E
E
a
13
Question 1

• If the compensation line were as shown, the
  worker would
• A. Work, and firm would profit
• B. Work, and firm would lose money
• C. Quit
• D. Cant Tell

C(E)
Net Rev Slope 1
E
a
14
Question 2

• If the compensation line were as shown, the
  worker would
• A. Work, and firm would profit
• B. Work, and firm would lose money
• C. Quit
• D. Cant Tell

C(E)
Net Rev Slope 1
E
a
15
Question 3

• If the compensation line were as shown, the
  worker would
• A. Work, and firm would profit
• B. Work, and firm would lose money
• C. Quit
• D. Cant Tell

C(E)
Net Rev Slope 1
E
a
16
Real World Examples

• Taxi drivers
• Net OutputCab fare-Gas
• Taxi driver pays daily rate for cab (a lt 0) and
  gets 100 commission on revenue net of other
  costs
• Farm workers
• Garment workers
• Sales people

17
Numerical Example

• Firm pays minimum to get needed effort, so
• aßEC(E)
• a6332 ?a -9

• Firm wants to pay w aßE
• Effort cost C(E)E2
• Each unit effort gives 2 units output sold for
  3/unit, so NR6E.
• Find E, a, ß
• Worker maximizesw-C(E) aßE-E2
• FOC ß-2E0 ?ß2E
• Firm chooses ß to max NetRev Cost
• Max (2)(3)E-(aßE)
• Max (2)(3)E-C(E)
• FOC yields 6-2E0
• E3, ß2E6

Net Rev Slope 6
NR(E)18
C(E)9
p(E)9
E3
E
ß6 (slope)
a-9
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Base salary plus commission

• Many commission workers dont pay for their job
• Receive base salary commission
• So a gt0
• Can this be optimal?
• Modified scheme
• Given compensation line (in red), does worker
  still choose E
• A. Yes
• B. No
• Worker chooses to do nothing and take base
  salary!

C(E)
Net Rev Slope 1
a
E
E
19
Question

• At Valleywag, what happens when writers have page
  views that place them below their base pay?
• A. The just earn less
• B. They receive reprimand
• C. They receive promotion

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Base salary plus commission

• Worker chooses to take base salary
• But what does firm do if worker consistently
  earns base salary?
• Fire the worker
• Commissions must exceed base for worker to keep
  job
• Given that worker must earn above base (a), does
  worker choose E?
• A. Yes
• B. No
• So modified scheme witha gt0 can elicit optimal
  effort.

C(E)
Net Rev Slope 1
a
E
E
21
Pay Commission on Total Revenue or Net Revenue?

• In theory, optimal commission is 100 of net
  revenue
• Usually see 100 commissions in practice?
• No, we see smaller of Total Revenue (Total
  Sales)
• Why?
• Net revenue hard to measure and verify
• Example Forest Gump
• So we see commissions of lt100 because they are
  usually defined relative to total revenue
• (This was not in the model)

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Quality vs. quantity

• http//www.youtube.com/watch?vV_gLOUbQZgkfeature
  related

23
Another Problem

• Different people have different C(E) function
• Optimal a for some might be suboptimal for
  others.
• How do you figure out workers C(E)?
• Experimentation
• Historical data
• Also difficult to figure out worker prod

24
Preference Falsification

• In standard model, firm pays worker minimum
  needed to elicit effort.
• So worker has an incentive not to reveal his true
  C(E)
• Work less, make it appear that C(E) is higher
• Get more pay for less work

C(E)
Net Rev Slope 1
E
E
Ef
A
a
25
Preference Falsification - Examples

• Matthewson
• Workers collude to restrict output
• Believe that firm will reduce pay scale if they
  reveal their willingness to work
• Valleywag
• Changes in page-view scale based on outcomes
• Note
• The examples show changes in commission rate ß,
  rather than the change in a, shown here, but the
  Idea is similar

C(E)
Net Rev Slope 1
E
E
Ef
A
a
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Disadvantages of Variable Pay (relative to Fixed
Pay)

• Piece rates encourage workers to run down capital
  stock
• Owner-driven taxis better maintained than rented
  taxis.
• Football free agency. Team more likely to let
  players get injured.
• Need to measure output. Can be costly.
• Piece rates encourage quantity over quality.
• Preference falsification
• Risk aversion Unpredictable events can give
  workers low outcomes, so workers may prefer
  salary to piece rateand work for less.
• Say no ones buying MP3 players this month
  because a festival of live bands is in town.
• With piece rates, I starve this month, with fixed
  salary Im OK.
• I may be willing to pay a premium for this
  stability and accept lower compensation.

27
Reducing Problems with Variable Pay

• Link pay to maintenance of capital stock. (Hard
  to monitor).
• Sell capital to workers.
• If CEOs focus too much on short term, link
  compensation to stock value.
• Other PROBLEMS with options.