The Encyclopedia of Economic Principals

Chapter 78

Rent-Seeking, Regulation, Capture, and Jurisdictional Arbitrage

Price the political choice, then count which costs are real and which are transfers.

Four of the chapter's worked examples, made interactive: a Peltzman markup as consumers organize, a tariff sold to a lobby, the resources burned in a rent-seeking contest, and a usury cap with fees and collateral. 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

Peltzman markup and consumer organization

How far does the regulated price fall when consumers become better organized?

The regulator balances producer support against consumer opposition. Stronger consumer organization steepens the opposition line, so the lines cross at a lower markup. Whether the resulting price keeps the service viable is a separate check.

Equation, written in LaTeX: P(m)=10m-\frac{1}{2}m^2,

Equation, written in LaTeX: O(m)=1.25m^2.

Equation, written in LaTeX: M(m)=10m-1.75m^2.

Equation, written in LaTeX: 10-m=2.5m,

Equation, written in LaTeX: m^*=\frac{20}{7}\approx2.86.

Equation, written in LaTeX: 10-m=5m,

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m is the authorized markup over the 15 dollar competitive benchmark. Producer support is 10m - m^2/2 and consumer opposition is k m^2, so the regulator sets 10 - m = 2km. The service needs at least 17.25 dollars to cover fixed cost.

Predict first. If consumer opposition doubles from k = 1.25 to 2.5, does the chosen price fall below the 17.25 floor?

Your prediction

Choose an example

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Figure: Peltzman markup and consumer organization. Left: the falling producer return line and the rising opposition line cross at markup 2.86. Right: the chosen price $17.86 against the benchmark $15.00 and the floor $17.25.
Consumer opposition coefficient k: 1.25
Constructed example: the chapter's hypothetical regulated service (benchmark 15, support slope 10, k = 1.25 and 2.5, floor 17.25); k = 0.75 and 1.75 are added for comparison.

Calculated values

Markup m*
2.86
Price
$17.86
Gap to floor
0.61
Viable at the floor
yes

Hypothetical teaching numbers, not market data. Setting marginal producer return equal to marginal consumer opposition gives 10 - m = 2.50m, so m* = 10 / 3.50 = 2.86 and the price is 15 + 2.86 = 17.86. $17.86 covers the $17.25 floor.

Worked steps

  1. 10 - m = 2 x 1.25 x m, so 10 = 3.50 m
  2. m* = 10 / 3.50 = 2.86
  3. Price = 15 + 2.86 = 17.86
  4. Price minus floor = 17.86 - 17.25 = 0.61

Use the idea

Before reading a regulated price as capture, compute the price that covers cost and ask whether the political balance could even reach it.

Where the conclusion applies

Quadratic support and opposition with fixed coefficients, a single regulated price and no change in cost or demand.

Check your understanding: At k = 2.5, what are m* and the price, and is the price viable?
10 - m = 5m gives m* = 10/6 = 1.67 and price 16.67, below 17.25, so it is not viable; the price falls by 17.86 - 16.67 = 1.19.

Chapter 78 source: section "Peltzman regulatory equilibrium".

Demonstration 2 of 4

Protection for sale and counter-lobbying

When does a producer contribution buy a tariff, and what does a rival lobby change?

The government compares the producer offer net of its weighted welfare loss with what the other side offers. A higher welfare weight or an organized counter-lobby raises the price of protection.

Equation, written in LaTeX: 2.5(900-870)=75.

Equation, written in LaTeX: 120-90=30

Equation, written in LaTeX: 4(30)=120.

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National welfare is 900 under free trade and 870 with the tariff. a is the political weight on each welfare unit. Producers gain 120 from the tariff and offer 90 if it is adopted; downstream users may offer d for free trade.

Predict first. With a = 2.5 and downstream users offering 20, does the producer offer of 90 still win?

Your prediction

Choose an example

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Figure: Protection for sale and counter-lobbying. Three bars: the tariff option is worth 15.00, the free-trade option 0.00, and the lobby keeps 30.00.
Government weight on welfare a: 2.5, Downstream offer for free trade: 0
Constructed example: the chapter's hypothetical tariff (welfare 900 and 870, gain 120, offer 90, a = 2.5 and 4, downstream offer 20); a = 1.5 and a downstream offer of 40 are added for comparison.

Calculated values

Weighted welfare loss
75.00
Tariff advantage
15.00
Downstream offer
0.00
Choice
Tariff
Producer offer needed
more than 75.00

Hypothetical teaching numbers, not market data. The tariff costs 2.50 x (900 - 870) = 75.00 weighted units, so the 90 offer leaves an advantage of 90 - 75.00 = 15.00. Against a downstream offer of 0.00, the tariff wins, 15.00 against 0.00, and producers keep 120 - 90 = 30.00. A winning producer offer must exceed 75.00 + 0.00 = 75.00, leaving producers less than 120 - 75.00 = 45.00.

Worked steps

  1. Weighted loss = 2.50 x (900 - 870) = 75.00
  2. Tariff advantage = 90 - 75.00 = 15.00
  3. Compare with the downstream offer 0.00: the tariff wins, 15.00 against 0.00, and producers keep 120 - 90 = 30.00
  4. Needed offer: more than 75.00 + 0.00 = 75.00

Use the idea

To judge whether a lobby can buy a policy, compute the weighted welfare loss plus any rival offer and compare it with the lobby's gross gain.

Where the conclusion applies

A binary choice, contributions paid only if the policy is adopted, and fixed welfare numbers.

Check your understanding: At a = 2.5 and a downstream offer of 20, what producer offer is needed and how much gain is left?
More than 75 + 20 = 95, leaving producers less than 120 - 95 = 25. At 90 the tariff advantage is 15 < 20, so free trade wins.

Chapter 78 source: section "Protection-for-sale model".

Demonstration 3 of 4

Tullock contest dissipation

How much of a 1,200 license rent is burned in the contest to win it?

Each firm's effort falls as rivals are added, but total effort rises toward the full rent. Only real resources enter the social-cost ledger; the license payment itself is a transfer.

Equation, written in LaTeX: x_i^*=\frac{5-1}{5^2}(1{,}200)=192.

Equation, written in LaTeX: X^*=5(192)=960.

Equation, written in LaTeX: 960+260+60=1{,}280.

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R = 1,200 is the license rent and n identical firms compete in a proportional contest. x* is each firm's effort and X* = n x* total effort. Monopoly deadweight is 260 and administration 60.

Predict first. Does adding contestants raise or lower total contest effort?

Your prediction

Choose an example

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Figure: Tullock contest dissipation. A stacked bar of social cost 1,280.00: acquisition 960.00, deadweight 260 and administration 60, beside a hatched bar for the 1,200 transfer.
Number of contestants: 5, Allocation: Influence contest
Constructed example: the chapter's hypothetical license (R = 1,200, five firms, deadweight 260, administration 60, auction bid cost 35, information 150); two, three and eight firms are added for comparison.

Calculated values

Effort per firm x*
192.00
Total contest effort X*
960.00
Expected net payoff per firm
48.00
Acquisition resources
960.00
Social cost
1,280.00

Hypothetical teaching numbers, not market data. With 5 firms each spends (5 - 1)/5^2 x 1,200 = 192.00, so the contest burns 960.00 of resources. The ledger is 960.00 + 260 + 60 = 1,280.00; the 1,200 license rent is a transfer and is not added again.

Worked steps

  1. x* = (5 - 1) / 5^2 x 1,200 = 4/25 x 1,200 = 192.00
  2. X* = 5 x 192.00 = 960.00
  3. Expected net = 1,200 / 5 - 192.00 = 240.00 - 192.00 = 48.00
  4. Acquisition resources = 5 x 192.00 = 960.00
  5. Social cost = 960.00 + 260 + 60 = 1,280.00

Use the idea

Separate gross lobbying spending, its useful by-products and pure transfers before calling any of it waste.

Where the conclusion applies

Identical risk-neutral firms, a proportional contest success function and a fixed rent.

Check your understanding: With 8 contestants, what is total effort and the social-cost ledger?
x* = 7/64 x 1,200 = 131.25 and X* = 1,050; the ledger is 1,050 + 260 + 60 = 1,370; each firm nets 150 - 131.25 = 18.75.

Chapter 78 source: section "Rent-Seeking, Monopoly, and Regulatory Capture".

Demonstration 4 of 4

Usury cap, hidden fees, and collateral

When does a rate cap shut out a loan, and which responses reopen it?

The cap limits the stated interest, not the cost of lending. A lender can respond with fees outside the legal definition, with real cost reductions, or by refusing the loan.

Equation, written in LaTeX: I^*=\$25+\$55+\$20=\$100,

Equation, written in LaTeX: r^*=\frac{\$100}{\$500}=20\%.

Equation, written in LaTeX: 0.12(\$500)=\$60,

Equation, written in LaTeX: \$60+\$50=\$110,

Equation, written in LaTeX: \$25+\$15+\$20+\$10=\$70,

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A one-year loan of L = 500 dollars costs 25 to fund and administer, 55 in expected default loss and a 20 dollar normal return. I* is the break-even charge and r* its rate. Collateral cuts default loss to 15 at a cost of 10; better data saves 10 of administration.

Predict first. Does collateral alone make the loan feasible at a 12 percent cap?

Your prediction

Choose an example

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Figure: Usury cap, hidden fees, and collateral. Two stacked bars: the required charge 100 built from its cost components and the allowed charge 60, with the cap line at 60.
Rate cap: 12%, Contract: Plain loan
Constructed example: the chapter's hypothetical 500 dollar loan (costs 25, 55 and 20, cap 12 percent, fee 50, collateral 15 and 10, data saving 10); caps of 16 and 20 percent are added for comparison.

Calculated values

Required charge
$100.00
Required rate
20%
Permitted interest
$60.00
Charge collected
$60.00
Shortfall
$40.00
Decision
Reject

Hypothetical teaching numbers, not market data. The break-even charge is 25 + 55 + 20 = 100, a rate of 20%. A 12% cap permits 0.12 x 500 = 60; the lender is short by 40.00 and rejects the loan.

Worked steps

  1. Required = 25 + 55 + 20 = 100, or 100 / 500 = 20%
  2. Permitted = 0.12 x 500 = 60
  3. Required minus collected = 100 - 60 = 40

Use the idea

When a rate cap binds, ask whether lending continues through fees, through collateral and data, or not at all; each has a different welfare meaning.

Where the conclusion applies

One period, known cost components and a cap that applies only to stated interest.

Check your understanding: With collateral, what is the required charge and rate, and the gap at 12 percent?
25 + 15 + 20 + 10 = 70, or 14 percent; 70 - 60 = 10 short. With the 10 dollar data saving the charge is 60, exactly the cap, so the loan breaks even.

Chapter 78 source: section "Usury Caps & Regulatory Arbitrage".