The Encyclopedia of Economic Principals

Chapter 73

Property Rights, Transaction Costs, and the Coasean Framework

Rights, bargaining costs and governance decide who does what.

Four of the chapter's worked examples, made interactive: Coase bargaining over a drone route, a corrective charge for smoke damage, ownership and hold-up, and the make-or-buy choice. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

Coase bargaining over a night drone route

Does the assignment of a legal right change whether the route runs?

With costless bargaining the efficient outcome happens under either right; only the payments differ. Once a bargain is costly, the outcome sticks at the baseline whenever the gain from moving is smaller than the cost, and then the right decides the allocation.

Equation, written in LaTeX: 140-85=55,

Equation, written in LaTeX: 140-100=40

Equation, written in LaTeX: 100-85=15

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The route earns the operator 140 and disturbs a resident by the harm shown. The right holder sets the baseline: with a right to fly the route runs unless the resident buys it out; with a right to quiet it stops unless the operator buys permission. A bargain also costs the transaction cost shown.

Predict first. With harm 170 and a right to fly, does the inefficient route keep operating once bargaining costs 40?

Your prediction

Choose an example

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Figure: Coase bargaining over a night drone route. Bars for the operator's profit 140 and the resident's harm 85. With a right to fly and a bargaining cost of 0, the route operates, which is efficient.
Resident disturbance: 85, Who holds the right: Operator: right to fly, Transaction cost of a bargain: 0
Constructed example: the chapter's hypothetical drone route (profit 140, harm 85 and 170, payment 100, bargaining cost 0 and 40) are the book's; a harm of 120 is added for comparison.

Calculated values

Joint surplus from operating
55
Efficient outcome
Operate
Baseline under the right
Operate
Gain from bargaining away from it
0
Final outcome
Operate
Efficient?
Yes

Operating is efficient: 140 - 85 = 55. With a right to fly the baseline is that the route operates, which is already efficient, so no trade is needed.

Worked steps

  1. Joint surplus from operating = 140 - 85 = 55
  2. Baseline with a right to fly: the route operates
  3. The baseline is already efficient, so there is nothing to buy
  4. Outcome: route operates

Use the idea

Before relying on private bargaining to fix a conflict, compare the joint gain from changing the outcome with the legal and enforcement cost of the deal.

Where the conclusion applies

Two parties, known values, no wealth effects and a single bargaining cost. Many affected parties or hidden values raise the cost of a deal.

Check your understanding: What is the gain from shutdown when harm is 170, and can it cover a 40 transaction cost?
Shutdown gain = 170 - 140 = 30; 30 < 40, so with a right to fly the route operates. With a right to quiet shutdown is the baseline and needs no trade.

Chapter 73 source: section "Coase theorem".

Demonstration 2 of 4

Smoke damage and the corrective charge

Which per-unit charge makes a producer stop at the efficient quantity?

A charge equal to the damage per unit makes the producer face the social cost, so it stops where price covers social marginal cost. A charge set below or above the damage leaves too many or too few units.

Equation, written in LaTeX: 40-19=21, 40-27=13, 40-35=5.

Equation, written in LaTeX: W(3)=120-54-27=39.

Equation, written in LaTeX: W(4)=160-88-36=36.

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Each unit sells for 40 and has private marginal cost 10, 18, 26, 34 or 42. Every unit causes the smoke damage shown, and the producer pays the per-unit charge shown. W(q) is the price times q less the private costs and the damage of the first q units.

Predict first. If damage per unit were 15 but the charge stayed at 9, how many units would the producer make, and is that efficient?

Your prediction

Choose an example

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Figure: Smoke damage and the corrective charge. Bars for units 1 to 5: private cost, cost including the charge of 9, and social cost with damage 9, against a price line at 40. The producer makes 3 units; the efficient quantity is 3.
Damage per unit: 9, Per-unit charge: 9
Constructed example: the chapter's hypothetical producer (price 40, costs 10 to 42, damage 9, charges 0 and 9) are the book's; damages 0, 5 and 15 and a charge of 15 are added for comparison.

Calculated values

Units made under the charge
3
Efficient quantity
3
Welfare at the chosen quantity
39
Welfare at the efficient quantity
39
Loss from the wrong quantity
0
Charge revenue
27

With damage 9 per unit, social marginal costs are private costs plus 9. W(3) = 120 - 54 - 27 = 39, against 39 at the efficient quantity. The charge of 9 makes the producer stop at the efficient 3 units, so no surplus is lost.

Worked steps

  1. Social margins 40 - (cost + 9) for units 1 to 5: 21, 13, 5, -3, -11
  2. Efficient quantity: every unit with a positive margin, so 3
  3. The producer faces cost + 9 and makes every unit below 40: 3
  4. W(3) = 3 x 40 - (10 + 18 + 26) - 3 x 9 = 120 - 54 - 27 = 39

Use the idea

Set a corrective charge from the measured damage per unit, and revisit it when damage changes with exposure.

Where the conclusion applies

Whole units, a fixed price, constant damage per unit and a producer who takes the charge as given. A unit whose cost equals the price exactly is not made.

Check your understanding: With no charge and damage 9, what is welfare at the private choice?
The producer makes 4 units (34 < 40 < 42); W(4) = 160 - (10 + 18 + 26 + 34 = 88) - 36 = 36.

Chapter 73 source: section "Externalities".

Demonstration 3 of 4

Ownership and hold-up in incomplete contracts

Does giving one party the asset raise total surplus when both must invest?

Each party invests until its own share of the marginal return equals its marginal cost. Moving the asset to one party raises that party's share and lowers the other's, so the change in total surplus depends on whose investment matters more.

Equation, written in LaTeX: c_A(a)=\frac{a^2}{2}, c_B(b)=\frac{b^2}{2}.

Equation, written in LaTeX: 0.5(8)=a, 0.5(8)=b,

Equation, written in LaTeX: 8(6)+8(2)-\frac{6^2}{2}-\frac{2^2}{2}=44.

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a and b are the two parties' investments, which a court cannot verify. Each unit adds 8 to value and costs a^2/2 or b^2/2. Each party keeps the share shown of its own marginal contribution, so it invests that share times 8.

Predict first. Giving A ownership (A keeps 0.75, B keeps 0.25) raises A's investment. Does total surplus rise?

Your prediction

Choose an example

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Figure: Ownership and hold-up in incomplete contracts. Left: investments a = 4 and b = 4 against the first-best 8. Right: total net surplus 48 against the first-best 64.
A's marginal share: 0.50, B's marginal share: 0.50
Constructed example: the chapter's hypothetical parties (contribution 8, shares 0.5 and 0.5, 0.75 and 0.25, and full shares) are the book's; an A share of 0.25 is added for comparison.

Calculated values

A's investment a
4
B's investment b
4
Total net surplus
48
First-best surplus
64
Shortfall from first best
16

A keeps 0.50 and B keeps 0.50 of their marginal contributions, so a = 0.50 x 8 = 4 and b = 0.50 x 8 = 4. Net surplus is 8(4) + 8(4) - 4^2/2 - 4^2/2 = 32 + 32 - 8.00 - 8.00 = 48, 16 below the first-best 64. A party that keeps only part of its marginal return invests less than 8, and each shortfall in investment costs surplus. Ownership is judged by total surplus, not by the owner's response alone.

Worked steps

  1. a = 0.50 x 8 = 4
  2. b = 0.50 x 8 = 4
  3. Net surplus = 8(4) + 8(4) - 4^2/2 - 4^2/2 = 32 + 32 - 8.00 - 8.00 = 48
  4. Shortfall = 64 - 48 = 16

Use the idea

When choosing who should own a shared asset, weigh the investment it encourages in the owner against the investment it discourages in the other party.

Where the conclusion applies

Equal marginal contributions of 8, quadratic costs and fixed shares. If A's investment were much more productive, ownership by A could rank first.

Check your understanding: What is total net surplus with A's share 0.75 and B's share 0.25?
a = 0.75 x 8 = 6 and b = 0.25 x 8 = 2; 48 + 16 - 18 - 2 = 44, which is 4 below balanced governance.

Chapter 73 source: section "Incomplete Contracts".

Demonstration 4 of 4

Make or buy with transaction costs

When does it pay to make a component inside the firm rather than buy it?

The choice between market and firm compares full governance costs, not production cost alone. The market has the cheaper production here, so it wins whenever contracting and adaptation costs are low enough.

Equation, written in LaTeX: TC_M=2{,}160+150+360+220+520=3{,}410.

Equation, written in LaTeX: TC_F=2{,}640+260+170+220=3{,}290.

Equation, written in LaTeX: TC_M'=2{,}160+150+80+220+160=2{,}770.

Scroll sideways for the whole equation

TC_M is the total cost of buying 120 components (production at 18 each plus search, drafting, monitoring and expected adaptation). TC_F is the cost of making them (production at 22 each plus management, measurement and expected delay and rigidity).

Predict first. If a standard template cuts drafting to 80 and adaptation to 160, which governance wins and by how much?

Your prediction

Choose an example

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Figure: Make or buy with transaction costs. Stacked bars of governance cost: buying from the market costs 3,410 with drafting 360 and adaptation 520; making inside the firm costs 3,290.
Outside drafting cost: 360, Expected adaptation cost: 520
Constructed example: the chapter's hypothetical manufacturer (120 components, every cost component, drafting 360 and 80, adaptation 520 and 160) are the book's; drafting 220 and adaptation 340 and 700 are added for comparison.

Calculated values

Market cost TC_M
3,410
Firm cost TC_F
3,290
Cheaper governance
Make (firm)
Saving from the cheaper option
120

TC_M = 2,160 + 150 + 360 + 220 + 520 = 3,410 and TC_F = 3,290. Making inside the firm saves 120, even though its physical production costs 480 more, because outside contracting is expensive. The component did not change; only the cost of governing the exchange did.

Worked steps

  1. TC_M = 2,160 + 150 + 360 + 220 + 520 = 3,410
  2. TC_F = 2,640 + 260 + 170 + 220 = 3,290
  3. Gap = 3,410 - 3,290 = 120

Use the idea

Before integrating a supplier, list the contracting and adaptation costs of buying and the management and rigidity costs of making, and compare the totals.

Where the conclusion applies

Fixed volume of 120, known cost components and no differences in quality, capacity or strategic control. Those would need their own entries.

Check your understanding: What is TC_M with drafting 80 and adaptation 160?
2,160 + 150 + 80 + 220 + 160 = 2,770; outsourcing is 3,290 - 2,770 = 520 cheaper.

Chapter 73 source: section "Transaction Costs".