Demonstration 1 of 4
Strict liability versus negligence and activity level
Both rules induce due care, so why do they produce different activity levels?
Strict liability puts the expected harm on the firm for every unit, so its activity choice reflects the full social cost. Negligence only asks whether care was due, so a careful firm expands activity as if its residual harm were free.
Scroll sideways for the whole equation
z is route units and B(z) the firm's benefit. Low care costs 2 per unit with expected harm 9; due care costs 5 with the expected harm shown. Under strict liability the firm pays all harm; under negligence a firm that takes due care pays none.
Predict first. Both rules induce due care. Which yields more route units?
Choose an example
Scroll sideways for the whole figure
Constructed example: the chapter's hypothetical delivery firm (benefit 24z - z^2/2, low care 2 and 9, due care 5 and 3) is the book's; due-care harms of 1 and 5 and the lost-surplus triangle are added for comparison.
Calculated values
- Social cost per unit, low care
- 11
- Social cost per unit, due care
- 8
- Care chosen
- Due care
- Firm's cost per unit
- 8
- Route units z
- 16
- Efficient units
- 16
- Excess units
- 0
- Lost surplus (red triangle)
- 0.00
Under strict liability the firm takes due care, since 5 + 3 = 8 is below 2 + 9 = 11. The firm pays for the harm, so it faces the full social cost 8 and chooses z = 24 - 8 = 16, the efficient level. Both rules get care right; only strict liability also gets the activity level right.
Worked steps
- Social cost per unit: low care 2 + 9 = 11, due care 5 + 3 = 8
- Strict liability: the firm bears 5 + 3 = 8 per unit and picks due care
- 24 - z - 8 = 0 gives z = 16
Use the idea
Where activity level matters as much as care, as with frequent risky operations, prefer a rule or a regulation that makes the actor bear residual harm.
Where the conclusion applies
A court that sets due care correctly, known expected harms and a linear marginal benefit. If regulation fixed activity at 16, both rules would give the same outcome.
Check your understanding: Under negligence, what is z, and why is it too high?
Chapter 74 source: section "Strict-liability versus negligence result".
Demonstration 2 of 4
Expectation damages and efficient breach
When do damages make a seller perform exactly when performing is efficient?
With damages equal to the buyer's expectation, the shop's choice compares P - C with -(V - P), which is the same as comparing V with C. Damages set too low invite wasteful breach; damages set too high force wasteful performance.
Scroll sideways for the whole equation
The shop sells a part at P = 80 to a buyer who values it at V = 125. C is the shop's realized cost and D the damages a court awards for breach. Expectation damages are V - P = 45.
Predict first. With cost 100, what happens if the court awards only 15?
Choose an example
Scroll sideways for the whole figure
Constructed example: the chapter's hypothetical machine shop (price 80, value 125, costs 100 and 150, damages 45, 15 and 80) is the book's; a cost of 125 is added for comparison.
Calculated values
- Expectation damages V - P
- 45
- Payoff from performing
- -20
- Payoff from breaching
- -45
- Shop's choice
- Perform
- Efficient choice
- Perform
- Social value lost
- 0
Performing pays 80 - 100 = -20; breaching costs the damages 45. Since -20 > -45, the shop performs. That matches the efficient choice: 25 of social value is created.
Worked steps
- Expectation damages = 125 - 80 = 45; damages awarded = 45
- Perform: 80 - 100 = -20; breach: -45
- Social comparison: value 125 against cost 100, difference 25
Use the idea
When setting or negotiating damages, aim at the promisee's lost expectation, since a mismeasured award distorts the performance decision.
Where the conclusion applies
Known values, full payment of damages and no transaction cost. Resale to a second buyer, which the chapter also discusses, is left out here.
Check your understanding: At cost 150 and damages 80, does the shop perform, and is that efficient?
Chapter 74 source: section "Expectation-damages efficient-performance result".
Demonstration 3 of 4
Becker deterrence: probability vs severity
Does catching more often or fining more heavily deter fare evasion, and what if fines go unpaid?
The rider compares the gain with the moral cost plus the expected sanction. Detection and severity enter as a product, but severity counts only for the part that is actually collected.
Scroll sideways for the whole equation
A rider gains 40 a month from evading and bears a moral cost of 6. p is the detection probability, F the stated penalty and the collected share the part of F actually paid. The expected sanction is p times the collected penalty.
Predict first. Does raising detection to 25 percent deter this rider (penalty 150, fully collected)?
Choose an example
Scroll sideways for the whole figure
Constructed example: the chapter's hypothetical rider (gain 40, moral cost 6, penalties 150 and 470, detection 0.08 and 0.25, collection 40 percent) and the 1,000 riders spread from 0 to 60 are the book's; detection of 0.15 is added for comparison.
Calculated values
- Effective penalty
- 150
- Expected sanction
- 12.00
- Net payoff
- 22.00
- This rider
- Evades
- Expected riders evading (of 1,000)
- 800.0
With detection 0.08, a stated penalty of 150 and 100 percent collected, the expected sanction is 0.08 x 150 = 12.00. The net payoff 40 - 6 - 12.00 = 22.00 is positive, so this rider keeps evading. Across 1,000 riders with benefits spread evenly from 0 to 60, about 800.0 still evade. A stated penalty deters only to the extent it is detected and collected.
Worked steps
- Effective penalty = 1.00 x 150 = 150
- Expected sanction = 0.08 x 150 = 12.00
- Net payoff = 40 - 6 - 12.00 = 22.00
- Riders evading = 1,000 x (60 - 12.00) / 60 = 800.0
Use the idea
When choosing between more inspection and higher fines, compare expected sanctions using the share of fines that is actually collected.
Where the conclusion applies
Risk-neutral riders, a known detection probability and a uniform spread of benefits in the population. Citations may rise when inspection expands even as evasion falls.
Check your understanding: With p = 0.08, F = 470 and 40 percent collection, what is the payoff?
Chapter 74 source: section "Becker deterrence model of crime".
Demonstration 4 of 4
Prohibition risk premium
How do seizure, punishment and concealment raise the price of a banned good?
Enforcement raises the price through three channels: more seizure divides costs over fewer deliveries, punishment adds an expected cost, and suppliers spend more on concealment. A rise in ordinary production cost raises the price the same way, so a price observation alone cannot separate them.
Scroll sideways for the whole equation
A supplier pays the production cost, a concealment cost and an expected punishment per attempt, and a share of shipments is seized. The break-even delivered price is the cost per attempt divided by the share that gets through. Demand is Q = 1,800 - 10p.
Predict first. Can a price of 120 tell you whether enforcement got tougher?
Choose an example
Scroll sideways for the whole figure
Constructed example: the chapter's hypothetical market (costs 45 and 81, low and high enforcement, demand 1,800 - 10p) is the book's; a production cost of 63 is added for comparison.
Calculated values
- Seizure probability
- 0.20
- Cost per attempt
- 60
- Break-even price
- 75
- Quantity
- 1,050
Under low enforcement a supplier pays 45 + 7 + 8 = 60 per attempt and loses a share 0.20 of shipments, so the break-even price is 60 / 0.80 = 75 and buyers take 1,050.
Worked steps
- Cost per attempt = 45 + 7 + 8 = 60
- p = 60 / 0.80 = 75
- Q = 1,800 - 10 x 75 = 1,050
Use the idea
Before reading a higher street price as evidence of tougher enforcement, check what happened to ordinary production and transport costs.
Where the conclusion applies
Competitive, risk-neutral suppliers with constant costs and linear demand. If demand at the break-even price were zero, the market would close.
Check your understanding: Under low enforcement with production cost 81, what is the price?
Chapter 74 source: section "Prohibition risk premium".