4.2 — An Economic Model of Precaution

# 4.2 — An Economic Model of Precaution
## ECON 315 • Economics of the Law • Spring 2021
### Ryan Safner Assistant Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/lawS21">ryansafner/lawS21</a> <a href="https://lawS21.classes.ryansafner.com"> lawS21.classes.ryansafner.com</a>

---

# Outline

### [Precaution: An Economic Model](#3)
### [No Liability](#)
### [Strict Liability](#)
### [Negligence](#)
### [A Family of Negligence Rules](#)
### [Comparing Negligence Rules, A Discrete Example of Bilateral Caution](#)

---

# Precaution: An Economic Model

---
# Precaution

.pull-left[
.smallest[
- As usual, our main concern is with the incentives these various liability rules create

- For torts, focus on parties' incentive to invest in (costly) precaution to avoid accidents
  - Driving/bicyling carefully, installing seatbelts, airbags, wearing helmets, etc.
  - Inspecting products carefully, quality control, independent audits, mandatory work breaks
  - All of these things are **costly** to parties, so there must be some **efficient** level
]
]

# Precaution

.pull-left[
- Speed like hell, drive drunk, texting
- Bicycle in the dark wearing black, no helmet
- Manufacture cheap, shoddy product quickly

]

.pull-right[
- Drive slowly and soberly
- Bicycle wearing helmet and reflectors
- Manufacture slow, quality controlled & inspected product 
]
]

.smallest[
- .hi[Precaution]: any activity either party can do to reduce probability of an accident (or severity of damage)

- .hi-purple[How much precaution is efficient?]

- .hi-purple[How do we design the law to get this amount?]
]

---

# A Simple Economic Model of Accidents

.smallest[
- Our main example was a car hitting a bicyclist, in real life:
  - Driver probably has insurance
  - Some damage to bicycle and to driver’s car
  - Driver and bicyclist may not even know what the law is

- We will simplify a lot by assuming:
  - Only one party is harmed
  - Parties know the law
  - Parties don’t have any insurance (for now)
  - Focus only on one party’s precaution at a time
  
]
]

---

# A Unilateral Care Model

- Unilateral harm (just one victim)

- .hi[Precaution]: costly actions that make accident less likely
  - Could be taken by either .blue[victim] or .red[injurer]
  - We'll consider both, but one at a time
  
.center[
![](../images/precautiontime.png)
]
]

---

# A Unilateral Care Model: Definitions/Notation

- `$w$`: cost of each “unit” or precaution
  - total cost of precaution is `$wx$`

- `$p(x)$`: probability of an accident, given level of `$x$`
 - `$\frac{\partial p(x)}{\partial x} < 0$`

- `$A$`: cost of accident (to victim)
  - expected cost of accidents is `$p(x)A$`

- When we examine .red[injurer] we will use `$x$`, when we examine .blue[victim] we will use `$y$`
  - Your textbook uses `$x^i$` and `$x^v$`
]
]

# A Unilateral Care Model

- .green[Cost of precaution, `\$wx\$`]

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" />
]

---

# A Unilateral Care Model
.pull-left[

- .green[Cost of precaution, `\$wx\$`]

- .red[Cost of accidents, `\$p(x)A\$`]
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" />
]

---
# A Unilateral Care Model
.pull-left[

- .green[Cost of precaution, `\$wx\$`]

- .red[Cost of accidents, `\$p(x)A\$`]

- .blue[Total Social Cost `\$p(x)A+wx\$`]
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" />
]

---

# A Unilateral Care Model
.pull-left[

- .green[Cost of precaution, `\$wx\$`]

- .red[Cost of accidents, `\$p(x)A\$`]

- .blue[Total Social Cost `\$p(x)A+wx\$`]

- Efficient level of precaution:

`$$\min_{x} \ color{blue}{p(x)A+wx}$$`
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" style="display: block; margin: auto;" />
]

---

# A Unilateral Care Model
.pull-left[

- .green[Cost of precaution, `\$wx\$`]

- .red[Cost of accidents, `\$p(x)A\$`]

- .blue[Total Social Cost `\$p(x)A+wx\$`]

- Efficient level of precaution:

`$$\min_{x} \color{blue}{p(x)A+wx}$$`

- Optimum `$x^\star$`:

.smallest[
`$$\begin{align*} \color{green}{w} &= \color{red}{-p’(x)A}\\
\color{green}{\text{MSC of precaution}} &= \color{red}{\text{MSB of precaution}}\\ \end{align*}$$`
]
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" style="display: block; margin: auto;" />
]

---

# A Unilateral Care Model
.pull-left[

- The efficient level of precaution, `$x^\star$` minimizes .blue[total social cost]
  - Balances the tradeoff between the .red[benefit of reduced accident likelihood] and the .green[cost of increased precaution]

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-6-1.png" width="504" style="display: block; margin: auto;" />
]

---

# A Unilateral Care Model: Technical Note

.pull-left[
.smallest[
- We are thinking of bilateral precaution, just “one party at a time”; again: 
  - `$x$` represent level of precaution by .red[injurer]
  - `$y$` represent level of precaution by .blue[victim]

- Really, the social problem between both parties:
`$$\min_{x,y} p(x,y)A-wx-wy$$`

]
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-7-1.png" width="504" style="display: block; margin: auto;" />
]

---

# A Unilateral Care Model: Technical Note

`$$\min_x p(x,y)A-wx-wy \quad \text{ given y}$$`
which has same solution as 
`$$\min_x p(x)A-wx$$`
- Results will generally be efficient *given* what the other party is doing

]
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-8-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Effect of Liability Rules on Precaution

- We know the **efficient** level of precaution is `$x^\star$`, which minimizes total social cost

- Now let’s consider the effect of .hi-turquoise[different liability rules] have on the **chosen** amount of precaution
]

---

# No Liability

---

# No Liability

- .red[Injurer] pays nothing for accidents
  - Bears the .green[cost] of his precaution
  - But no .red[benefit] (of avoided damages)
  - **Has no incentive to take any precaution**

- .blue[Victim] bears cost of any accidents, plus cost of her precaution taken
  - .blue[Victim] precaution imposes no externality on .red[Injurer]
  - .blue[Victim] will invest in efficient amount of precaution `$y^\star$`
]
]
.pull-right[
.center[
![](../images/norules.jpg)
]
]

---

# No Liability

- .red[Injurer]'s private costs: `$\color{green}{wx}$`
`$$\min_{x} \color{green}{wx} \implies x_{NL}=0$$`

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-9-1.png" width="504" style="display: block; margin: auto;" />
]

---

# No Liability

- .red[Injurer]'s private costs: `$\color{green}{wx}$`
`$$\min_{x} \color{green}{wx} \implies x_{NL}=0$$`

- .blue[Victim]'s private costs: `$\color{blue}{p(y)A+wy}$`
`$$\min_{y} \color{blue}{p(y)A+wy} \implies y_{NL}=y^\star$$`
  - chooses efficient precaution

- Rule of .hi[no liability] leads to:
  - efficient precaution by .blue[Victims]
  - no precaution by .red[Injurers]
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-10-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Comparing Incentives Under Different Liability Rules

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution |
|------|---------|--------|
| No liability | Zero | .green[Efficient] |

---

# Determining Accidents

- Precaution isn't the only thing that affects the number of accidents
  - Precautions are extra actions that make our activity less dangerous

- Also the .hi-purple[amount of activities] we do affects the number of accidents
  - I decide how often to drive
  - You decide how often to bike

- Liability rules also create incentives for .hi-purple[activity levels]
]

---

# Determining Accidents: No Liability

- With .hi[no liability], I am not liable if I hit you
  - I don't consider cost of accident when I decide **how fast** to drive
  - nor when I decide **how much** to drive
  - .hi-purple[So I drive too recklessly *and* too often]

- My driving imposes a negative externality on others
  - With no liability, .red[Injurer]'s activity level is inefficiently high
]

.pull-right[
.center[
![](../images/Careless-Driving.jpg)
]
]
---
# Determining Accidents: No Liability

- With .i[no liability], you bear the full cost of an accident
  - More activity by victim (bicycling) leads to more accidents
  - You weigh cost of accidents when deciding **how carefully** to ride, and **how much** to ride
  - Your private cost equals the social cost
  - .hi-purple[You take the efficient level of precaution, and efficient level of activity]
]

# Comparing Incentives Under Different Liability Rules

---

# Strict Liability

---

# Strict Liability

.pull-left[
.smallest[
- Imagine a world of .hi[strict liability] (SL) with perfect compensation
  - `$D=A$` damages equal to the cost of the accident

- .red[Injurer] pays for any accidents he causes
  - Bears the full .red[cost of accidents] plus his .green[precautions] taken
  - Receives .red[benefit] (of avoided damages)
  - Internalizes externality his actions cause, chooses the efficient level of precaution

- .blue[Victim] is fully insured
  - Has **no incentive** to invest in any precaution
]
]

---

# Strict Liability

- .red[Injurer]'s private costs:  `$\color{blue}{p(x)A+wx}$`
`$$\min_{x} \color{blue}{p(x)A+wx} \implies x_{SL}=x^\star$$`
  - chooses efficient precaution

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-11-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Strict Liability

- .red[Injurer]'s private costs:  `$\color{blue}{p(x)A+wx}$`
`$$\min_{x} \color{blue}{p(x)A+wx} \implies x_{SL}=x^\star$$`
  - chooses efficient precaution

- .blue[Victim]'s private costs: `$\color{green}{wy}$`
`$$\min_{y} \color{green}{wy} \implies y_{SL}=0$$`
  
- Rule of .hi[strict liability] leads to:
  - efficient precaution by .red[Injurers]
  - no precaution by .blue[Victims]
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-12-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Comparing Incentives Under Different Liability Rules

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution |
|------|---------|--------|
| No liability | Zero | .green[Efficient] |
| Strict liability | .green[Efficient] | Zero |
---

# Strict Liability: Activity Levels

.pull-left[
.smallest[
- Under strict liability, .red[injurer] internalizes cost of accidents
  - Weighs benefit from driving against cost of accidents
  - Takes **efficient** activity level

- Under strict liability, .blue[victim] does not bear cost of accidents
  - Ignores cost of accidents when deciding how much to bicycle
  - Takes **inefficiently high** activity level

- .hi-purple[Strict liability leads to **efficient** level of injurer activity, **inefficiently high** level of victim activity]
]
]

---
# Comparing Incentives Under Different Liability Rules

---

# Comparing Incentives Under Different Liability Rules

- .hi[No liability] leads to **inefficient** behavior by .red[injurer], **efficient** behavior by .blue[victim]

- .hi[Strict liability] leads to **efficient** behavior by .red[injurer], **inefficient** behavior by .blue[victim]

- Like the .hi-purple[paradox of compensation] from contract law!
 - One rule sets multiple incentives...we can't get them all right
 - ...or can we? Tort law has this One Weird TrickTM
]
]

---

# Negligence

---

# Negligence

- .hi[Negligence rule]: .red[Injurer] is only liable **if he breached his duty of due care**
  - Put alternatively, liable only if accident is “his fault”

- Within our model: 
 - Legal standard of care `$x^l$`
 - .red[Injurer] owes damages if `$x < x^l$`
 - If `$x<x^l \rightarrow D=A$`
 - If `$x \geq x^l \rightarrow D=0$`

]

# Negligence

- Private cost to .red[injurer] is:

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-13-1.png" width="504" style="display: block; margin: auto;" />

]

---

# Negligence

- Private cost to .red[injurer] is:
`$$\begin{cases}
p(x)A+wx && \text{if } x<x^l\\
\end{cases}$$`

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-14-1.png" width="504" style="display: block; margin: auto;" />

]

---

# Negligence

- Private cost to .red[injurer] is:
`$$\begin{cases}
p(x)A+wx && \text{if } x<x^l\\
wx && \text{if } x \geq x^l\\
\end{cases}$$`

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-15-1.png" width="504" style="display: block; margin: auto;" />

]

---

# Negligence

- Private cost to .red[injurer] is:
`$$\begin{cases}
p(x)A+wx && \text{if } x<x^l\\
wx && \text{if } x \geq x^l\\
\end{cases}$$`

- If standard of care `$x^l$` is set to `$x^\star$`, .red[injurer] minimizes private cost by taking efficient caution
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-16-1.png" width="504" style="display: block; margin: auto;" />

]

---

# Negligence: Injurer Precaution

- What about .blue[victim]'s incentives?
  - We saw .red[injurer] will exercise due care and *not* be liable!
  - .blue[Victim] now bears cost of any accidents! (.hi-purple[residual risk])

- Private cost to .blue[victim] is: `$\color{blue}{p(y)A+wy}$`
  - .blue[Victim] chooses `$y^\star$`, efficient precaution too!
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-17-1.png" width="504" style="display: block; margin: auto;" />

]

---

# Comparing Incentives Under Different Liability Rules

---

# A Family of Negligence Rules

---

# Other Negligence Rules

.pull-left[
- The rule we just considered is “simple” negligence
  - Only consider .red[injurer]'s actions in determining liability

- But in deciding whether .red[injurer] should be liable, we could also consider whether the .blue[victim] was negligent

]
.pull-right[
.center[
![](../images/spidermannegligence.jpg)
]
]

---

# Contributory Negligence: Butterfield v. Forrester

- Forrester (Defendent) placed a pole in road next to his house while making repairs

- Butterfield (Plaintiff) was riding at high speed at night, hit the pole, fell off his horse, sued for damages

- Witness said that if Forrester had not been riding fast, would have seen the pole

- Jury ruled Plaintiff should not be able to collect damages from Plaintiff due to their own .hi[contributory negligence]

]
]

.smallest[
> “One person being in fault will not dispense with another’s using ordinary care for himself.”

]
]

---

# Injurer & Victim Negligence

- Let’s compare the whole family of negligence rules

- .red[Injurer] is **negligent/at fault** when they fail to take due care, `$x<x^*$`.magenta[†]

- .blue[Victim] is **negligent/at fault** when they fail to take due care, `$y<y^*$`.magenta[†]

- Now let’s consider who is **liable** for the accident under various negligence rules

.tiny[.magenta[†] Assuming standards of care are set at the efficient levels `\$x^l=x^\star\$` and `\$y^l=y^\star\$`]

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-18-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Simple Negligence

- **Simple negligence**:

- .red[Injurer] is liable if they do not take due care `$x<x^*$`

- .red[Injurer] is *not* liable if they *do* take due care `$x \geq x^*$`
  - .blue[Victim] cannot collect damages for any accident
    
]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-19-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Negligence With a Defense of Contributory Negligence

- **Negligence with a defense of Contributory Negligence**:

- .red[Injurer] is liable if they do not take due care `$x<x^*$`

- .red[Injurer] is *not* liable if .blue[Victim] does not take due care `$y<y^*$`

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-20-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Comparative Negligence

- **Comparative Negligence**: if both parties are negligent, they share the cost of the accident (possibly proportionately)
  - e.g. if accident cause was 70% .red[injurer]’s fault, 30% .blue[victim]’s fault, .red[injurer] pays for 70% of damages

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-21-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Strict liability with Contributory Negligence

- **Strict liability with defense of Contributory Negligence**:

- .red[Injurer] is liable (regardless of their level of precaution `$x)$` *unless* .blue[Victim] does not take due care `$y<y^*$`

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-22-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Family of Negligence Rules

.pull-left[
<img src="4.2-slides_files/figure-html/unnamed-chunk-23-1.png" width="504" style="display: block; margin: auto;" />

]

.pull-right[
<img src="4.2-slides_files/figure-html/unnamed-chunk-25-1.png" width="504" style="display: block; margin: auto;" />

]

- .hi-purple[Any of these rules (with efficient standard of care) incentivize efficient precaution by both parties!] `$(\color{blue}{x^\star}, \color{red}{y^\star})$`
]

---

# Comparing Negligence Rules, A Discrete Example of Bilateral Caution

---

# Discrete Example of Bilateral Precaution

- Each party .red[Injurer] and .blue[Victim] can either take **precaution** or **not**
  - Precaution costs each party $20
  - Each accident costs $1,000 in harm

- Chance of accident is:
  - 10% if nobody takes precaution
  - 6% if one party takes precaution
  - 2% if both parties take precaution

- Note: precaution is efficient for each party: costs $20; reduces expected damage by 0.04($1,000) = $40
]
]
.pull-right[
.center[
![](../images/caution.jpg)
]
.quitesmall[
A: $1,000

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]

]

---

# Discrete Example of Bilateral Precaution

- .red[Injurer] is liable if he failed to take precaution...unless .blue[blue] victim failed too

]
]

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]
]

---

# Discrete Example of Bilateral Precaution

- .red[Injurer] is liable if he failed to take precaution...unless .blue[blue] victim failed too

- Notice .blue[Victim]'s dominant strategy is **Precaution**
  - If .red[Injurer] not taking precaution, .blue[victim] wants to avoid liability
  - If .red[Injurer] takes precaution, .blue[victim] bears residual risk, wants to minimize accidents

]
]
.pull-right[
.center[
![](../images/negligencegame2.png)

]

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]
]

---

# Discrete Example of Bilateral Precaution

- .red[Injurer] is liable if he failed to take precaution...unless .blue[blue] victim failed too

- For .red[Injurer], best response to .blue[Victim]'s precaution is precaution

- .hi-purple[Nash Eq.]: (.red[Precaution], .blue[precaution]), efficient!
]
]

]

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]
]

---

# Discrete Example of Bilateral Precaution

]

]

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]
]

---

# Discrete Example of Bilateral Precaution

- Notice .blue[Victim]'s dominant strategy is **Precaution**
]
]

]
.quitesmall[
A: $1,000

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]
]

---

# Discrete Example of Bilateral Precaution

- Notice .blue[Victim]'s dominant strategy is **Precaution**

- For .red[Injurer], best response to .blue[Victim]'s precaution is precaution

- .hi-purple[Nash Equilibrium]: (.red[Precaution], .blue[precaution]) and is efficient!
]
]

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]
]

---

# Discrete Example of Bilateral Precaution

- .red[Injurer] is liable regardless of his precaution ... unless .blue[blue] victim was negligent

]
]

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]

]

---

# Discrete Example of Bilateral Precaution

- .red[Injurer] is liable regardless of his precaution ... unless .blue[blue] victim was negligent

- Notice .blue[Victim]'s dominant strategy is **Precaution**
]
]

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]

]

---

# Discrete Example of Bilateral Precaution

- .red[Injurer] is liable regardless of his precaution ... unless .blue[blue] victim was negligent

- Notice .blue[Victim]'s dominant strategy is **Precaution**

- For .red[Injurer], best response to .blue[Victim]'s precaution is precaution

- .hi-purple[Nash Equilibrium]: (.red[Precaution], .blue[precaution]) and is efficient!
]
]

w: $20 (each party)

p: 10% (neither), 6% (one careful), 2% (both)
]
]

---

# Comparing Incentives Under Different Liability Rules

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero | .green[Efficient] | Too High | .green[Efficient] |
| Strict liability | .green[Efficient] | Zero | .green[Efficient] | Too High |
| (“Simple”) Negligence | .green[Efficient] | .green[Efficient] | | |
| Negligence w/Contributory Negligence | .green[Efficient] | .green[Efficient] | | |
| Comparative Negligence | .green[Efficient] | .green[Efficient] | | |
| Strict Liability w/Contributory Negligence | .green[Efficient] | .green[Efficient] | | |

Assuming all relevant standards of care are set at the efficient levels `$(x^l=x^*)$`

---

# Activity Levels under Negligence Rules

- **Simple negligence**: .red[injurer] liable if he was negligent

- Leads .red[injurer] to take efficient precaution, so **injurer expects to not be liable for any accidents**

- So .red[Injurer] ignores cost of accidents when deciding on activity level
  - Drives carefully, but still **drives too much**

- .blue[Victim] bears residual risk
  - Bikes carefully, and bikes **efficient amount**
]
]

# Comparing Incentives Under Different Liability Rules

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero | .green[Efficient] | Too High | .green[Efficient] |
| Strict liability | .green[Efficient] | Zero | .green[Efficient] | Too High |
| (“Simple”) Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Negligence w/Contributory Negligence | .green[Efficient] | .green[Efficient] | | |
| Comparative Negligence | .green[Efficient] | .green[Efficient] | | |
| Strict Liability w/Contributory Negligence | .green[Efficient] | .green[Efficient] | | |

Assuming all relevant standards of care are set at the efficient levels `$(x^l=x^*)$`

---

# Activity Levels under Negligence Rules

.pull-left[
.smallest[
- **Contributory Negligence** and **Comparative negligence**: efficient precaution by both parties

- Leads .red[injurer] to take efficient precaution, so **injurer expects to not be liable for any accidents**

- So .red[Injurer] ignores cost of accidents when deciding on activity level
  - Drives carefully, but still **drives too much**

- .blue[Victim] bears residual risk
  - Bikes carefully, and bikes **efficient amount**
]
]

---

# Comparing Incentives Under Different Liability Rules

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero | .green[Efficient] | Too High | .green[Efficient] |
| Strict liability | .green[Efficient] | Zero | .green[Efficient] | Too High |
| (“Simple”) Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Negligence w/Contributory Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Comparative Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Strict Liability w/Contributory Negligence | .green[Efficient] | .green[Efficient] | | |

Assuming all relevant standards of care are set at the efficient levels `$(x^l=x^*)$`

---

# Activity Levels under Negligence Rules

.pull-left[
.smallest[
- **Strict liability w/comparative negligence defense**: if .blue[victim] is not negligent, .red[injurer] is liable regardless of precaution

- Leads both parties to take efficient precaution, so .red[injurer] is residual risk bearer, and is **liable for any accidents**
  - So .red[injurer] weighs cost of accidents against benefits, drives **efficient amount**

- .blue[Victim], fully insured, ignores cost of accidents when deciding on activity level
  - Bikes carefully, but still **bikes too much**

]
]

# Comparing Incentives Under Different Liability Rules

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero | .green[Efficient] | Too High | .green[Efficient] |
| Strict liability | .green[Efficient] | Zero | .green[Efficient] | Too High |
| (“Simple”) Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Negligence w/Contributory Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Comparative Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Strict Liability w/Contributory Negligence | .green[Efficient] | .green[Efficient] | .green[Efficient] | Too High |

Assuming all relevant standards of care are set at the efficient levels `$(x^l=x^*)$`

---

# Comparing Incentives Under Different Liability Rules

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero | .green[Efficient] | Too High | .green[Efficient] |
| Strict liability | .green[Efficient] | Zero | .green[Efficient] | Too High |
| (“Simple”) Negligence | .b[.ul[.green[Efficient]]] | .green[Efficient] | .b[.ul[Too High]] | .green[Efficient] |
| Negligence w/Contributory Negligence | .b[.ul[.green[Efficient]]] | .green[Efficient] | .b[.ul[Too High]] | .green[Efficient] |
| Comparative Negligence | .b[.ul[.green[Efficient]]] | .green[Efficient] | .b[.ul[Too High]] | .green[Efficient] |
| Strict Liability w/Contributory Negligence | .green[Efficient] | .b[.ul[.green[Efficient]]] | .green[Efficient] | .b[.ul[Too High]] |

.smallest[
Highlighted cases: party takes precaution only to AVOID liability `$\implies$` precaution is efficient, but activity level is too high
]

---

# Comparing Incentives Under Different Liability Rules

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero | .b[.ul[.green[Efficient]]] | Too High | .b[.ul[.green[Efficient]]] |
| Strict liability | .b[.ul[.green[Efficient]]] | Zero | .b[.ul[.green[Efficient]]] | Too High |
| (“Simple”) Negligence | .green[Efficient] | .b[.ul[.green[Efficient]]] | Too High | .b[.ul[.green[Efficient]]] |
| Negligence w/Contributory Negligence | .green[Efficient] | .b[.ul[.green[Efficient]]] | Too High | .b[.ul[.green[Efficient]]] |
| Comparative Negligence | .green[Efficient] | .b[.ul[.green[Efficient]]] | Too High | .b[.ul[.green[Efficient]]] |
| Strict Liability w/Contributory Negligence | .b[.ul[.green[Efficient]]] | .green[Efficient] | .b[.ul[.green[Efficient]]] | Too High |

.smallest[
Highlighted cases: party reduces accidents, since they bear the cost, so both precaution & activity level are both efficient
]

---

# These Results Look Overwhelming

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero | .green[Efficient] | Too High | .green[Efficient] |
| Strict liability | .green[Efficient] | Zero | .green[Efficient] | Too High |
| (“Simple”) Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Negligence w/Contributory Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Comparative Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Strict Liability w/Contributory Negligence | .green[Efficient] | .green[Efficient] | .green[Efficient] | Too High |

These results look overwhelming, but really the result of four basic ideas

---

# These Results Look Overwhelming

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero |  | Too High |    |
| Strict liability |     | Zero |     | Too High |
| (“Simple”) Negligence |    |    |    |    |
| Negligence w/Contributory Negligence |    |    |    |    |
| Comparative Negligence |     |    |     |     |
| Strict Liability w/Contributory Negligence |     |     |     |     |

1) If you don’t bear any of the cost of accidents, you have no incentive to prevent them

---

# These Results Look Overwhelming

2) If you **do** bear the cost of accidents, you’ll do whatever you can to prevent them

---

# These Results Look Overwhelming

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero | .green[Efficient] | Too High | .green[Efficient] |
| Strict liability | .green[Efficient] | Zero | .green[Efficient] | Too High |
| (“Simple”) Negligence | .green[Efficient] |    | Too High |    |
| Negligence w/Contributory Negligence | .green[Efficient] |    | Too High |    |
| Comparative Negligence |.green[Efficient] |    | Too High |     |
| Strict Liability w/Contributory Negligence |     | .green[Efficient] |     | Too High |

3) If you can avoid liability by exercising due care, you’ll do it, but then you won’t reduce activity

---

# These Results Look Overwhelming

| Rule | .red[Injurer] Precaution | .blue[Victim] Precaution | .red[Injurer] Activity | .blue[Victim] Activity | 
|------|---------|--------|-----|-----|
| No liability | Zero | .green[Efficient] | Too High | .green[Efficient] |
| Strict liability | .green[Efficient] | Zero | .green[Efficient] | Too High |
| (“Simple”) Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Negligence w/Contributory Negligence | .green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Comparative Negligence |.green[Efficient] | .green[Efficient] | Too High | .green[Efficient] |
| Strict Liability w/Contributory Negligence | .green[Efficient] | .green[Efficient] |  .green[Efficient] | Too High |

4) If the other guy can duck liability with due care, you’re the residual risk bearer, and therefore you’ll take due care