The Encyclopedia of Economic Principals

Chapter 79

State Capacity, Extractive Institutions, and Development

Who decides, how long they expect to stay, and who keeps the gain.

Four of the chapter's worked examples, made interactive: a ruler's horizon and restraint, windfall claims under weak commitment, an extractive elite's tax choice, and an officeholder deciding on tax capacity. 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

Stationary bandit and survival horizon

When does a ruler restrain extraction and pay for a patrol?

A ruler who expects to stay values the future tax base, so restraint and public order pay. A short horizon shrinks the continuation weight and immediate extraction wins again.

Equation, written in LaTeX: R_H=0.75(60)=45.

Equation, written in LaTeX: R_M=0.35(110)=38.5.

Equation, written in LaTeX: 45+0.765(15)=56.475.

Equation, written in LaTeX: 38.5+0.765(38.5)=67.9525.

Equation, written in LaTeX: 45.5-8+0.765(45.5)=72.3075.

Scroll sideways for the whole equation

Heavy extraction yields 45 now and 15 next year; moderate extraction yields 38.5 in both years. A patrol costing 8 raises moderate revenue to 45.5. s is the ruler's survival probability and delta = 0.90 the discount factor, so next year is weighted by s x delta.

Predict first. At survival 0.20, which policy wins?

Your prediction

Choose an example

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Figure: Stationary bandit and survival horizon. Three bars of two-period expected revenue at survival 0.85: heavy 56.4750, moderate 67.9525, moderate plus patrol 72.3075; moderate plus patrol is highlighted.
Survival probability s: 0.85
Constructed example: the chapter's hypothetical district (revenues 45, 15, 38.5 and 45.5, patrol 8, delta 0.90, survival 0.85 and 0.20); survival 0.50 is added for comparison.

Calculated values

Continuation weight
0.765
Heavy
56.4750
Moderate
67.9525
Moderate plus patrol
72.3075
Best policy
Moderate plus patrol

Hypothetical teaching numbers, not historical data. With survival 0.85 the ruler weights next year by 0.85 x 0.90 = 0.765. Heavy extraction is worth 45 + 0.765(15) = 56.4750, moderate extraction 38.5 + 0.765(38.5) = 67.9525, and moderate extraction with the patrol 45.5 - 8 + 0.765(45.5) = 72.3075. The best policy is moderate plus patrol.

Worked steps

  1. Weight = 0.85 x 0.90 = 0.765
  2. Heavy = 45 + 0.765 x 15 = 56.4750
  3. Moderate = 38.5 + 0.765 x 38.5 = 67.9525
  4. Patrol = 45.5 - 8 + 0.765 x 45.5 = 72.3075
  5. Highest: Moderate plus patrol

Use the idea

When judging whether rulers will invest in order or restrain taxes, estimate their expected tenure as well as the revenue at stake.

Where the conclusion applies

Two periods, fixed revenue paths for each policy and risk neutrality; the values say nothing about whether the tax rate is socially optimal.

Check your understanding: At s = 0.20, what are the heavy and patrol values?
Weight 0.20 x 0.90 = 0.18; heavy 45 + 0.18(15) = 47.7; patrol 37.5 + 0.18(45.5) = 45.69; heavy wins.

Chapter 79 source: section "Olson stationary-bandit model".

Demonstration 2 of 4

Voracity effect and windfall claims

How can a windfall leave less for investment than before?

When groups cannot commit to restraint, each claims more than its share because it expects the others to escalate. Total claims can exceed the windfall, crowding out investment. A binding cap on new transfers breaks the escalation.

Equation, written in LaTeX: \frac{\Delta T}{\Delta W}=\frac{\$48}{\$30}=1.6.

Equation, written in LaTeX: \$180-\$60-\$93=\$27,

Equation, written in LaTeX: \$180-\$60-(\$45+\$18)=\$57.

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Normal resources are 150 dollars, committed services 60 and transfers to four blocs 45. A 30 dollar windfall W arrives and each bloc demands d more, so transfers T rise by 4d. Investment is what remains.

Predict first. Above what per-bloc demand does investment fall below 45?

Your prediction

Choose an example

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Figure: Voracity effect and windfall claims. Three stacked budget bars: before the windfall investment is 45; with weak commitment transfers are 93 and investment 27; under the cap investment is 57.
Extra demand per bloc ($): 12
Constructed example: the chapter's hypothetical economy (150, 60, 45, windfall 30, four blocs demanding 12, proportional 30 in total, cap 18); demands of 6 and 15 are added for comparison.

Calculated values

New claims
48.00
Transfers
93.00
Claim multiplier
1.6
Investment
27.00
Investment under the 18 cap
57.00

Hypothetical teaching numbers, not historical data. Each of four blocs demands 12 more, so transfers rise by 48 to 93 and the claim multiplier is 48/30 = 1.6. Investment is 180 - 60 - 93 = 27, so investment falls 18 below its pre-windfall 45: the voracity effect. A binding 18 cap keeps investment at 57.

Worked steps

  1. New claims = 4 x 12 = 48; transfers = 45 + 48 = 93
  2. Claim multiplier = 48 / 30 = 1.6
  3. Investment = 180 - 60 - 93 = 27
  4. With the 18 cap: 180 - 60 - (45 + 18) = 57

Use the idea

After a revenue windfall, compare the rise in claims with the windfall itself; a ratio above one signals voracity.

Where the conclusion applies

Fixed services, symmetric blocs and a cap that actually binds.

Check your understanding: If each bloc demands 15, what are the multiplier and investment?
Transfers 45 + 60 = 105; multiplier 60/30 = 2.0; investment 180 - 60 - 105 = 15. The threshold is 7.5 per bloc.

Chapter 79 source: section "Voracity effect".

Demonstration 3 of 4

Extractive elite tax choice

Why can a growth-raising arrangement be politically unattractive to the elite?

The elite maximizes its own revenue, which peaks at tau = 0.5, not total output. A project that raises output mostly benefits producers, so an elite paying the full cost turns it down.

Equation, written in LaTeX: y(\tau)=160(1-\tau),

Equation, written in LaTeX: R(\tau)=160\tau(1-\tau).

Equation, written in LaTeX: \frac{dR}{d\tau}=160(1-2\tau)=0,

Equation, written in LaTeX: 180(0.75)=135,

Equation, written in LaTeX: 33.75-30-8=-4.25,

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Potential output is e0 = 160; extraction at rate tau leaves output y = e0(1 - tau), of which the elite takes R = tau y. A public input costing 8, paid by the elite, raises potential output to 180.

Predict first. Will the elite fund an 8 unit input that raises net social output by 7 at tau = 0.25?

Your prediction

Choose an example

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Figure: Extractive elite tax choice. Output falls linearly from 160 as the extraction rate rises, and elite revenue is a hill peaking at tau = 0.5. At tau = 0.50 output is 80.00 and revenue 40.00.
Extraction rate tau: 0.5, Public input (cost 8): No input
Constructed example: the chapter's hypothetical economy (e0 = 160, tau 0.5 and 0.25, input 8 raising e0 to 180 at tau 0.25); tau = 0.75 and the input at tau 0.5 and 0.75 are added for comparison.

Calculated values

Output
80.00
Elite revenue
40.00
Producers keep
40.00

Hypothetical teaching numbers, not historical data. At tau = 0.50 output is 160(1 - 0.50) = 80.00, the elite takes 40.00 and producers keep 40.00. Revenue peaks where 160(1 - 2 tau) = 0, at tau = 0.5.

Worked steps

  1. y = 160 x (1 - 0.50) = 80.00
  2. R = 0.50 x 80.00 = 40.00
  3. Producers keep 80.00 - 40.00 = 40.00

Use the idea

When a socially productive reform stalls, compute the decisive group's private change separately from the social gain.

Where the conclusion applies

Linear output loss in the tax rate, an elite that pays the whole input cost and no change in who holds power.

Check your understanding: At tau 0.25 with the input, what is the elite's private change?
Output 180 x 0.75 = 135 and revenue 33.75; 33.75 - 30 - 8 = -4.25, so it rejects, although net social output rises from 120 to 127.

Chapter 79 source: section "Extractive Institutions".

Demonstration 4 of 4

Collection capacity and the officeholder's horizon

Why can a valuable tax-capacity project be rejected by the official who must pay for it?

The public value of better collection accrues over years, but an officeholder who may lose power counts only the part it expects to keep. Insecure tenure makes capacity building look unprofitable.

Equation, written in LaTeX: T_0=0.45(0.18)(\$2{,}000)=\$162.

Equation, written in LaTeX: T_1=0.70(0.18)(\$2{,}000)=\$252,

Equation, written in LaTeX: \$90(1+0.92+0.92^2)=\$248.976.

Equation, written in LaTeX: 0.40(\$90)=\$36,

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Revenue is T = q tau B with base B = 2,000 dollars, statutory rate tau = 0.18 and collection capacity q. A 50 dollar project raises q from 0.45. Future gains are discounted by 0.92 a year over three years. p is the officeholder's probability of keeping control next year.

Predict first. At capacity 0.70, does a retention probability of 0.60 make the officeholder invest?

Your prediction

Choose an example

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Figure: Collection capacity and the officeholder's horizon. Four bars: annual gain 90.00, three-year present value 248.976, the officeholder's expected benefit 36.00 and the cost 50, with a dashed line at the 50 cost.
Capacity after the project: 0.7, Retention probability p: 0.4
Constructed example: the chapter's hypothetical economy (base 2,000, rate 0.18, capacity 0.45 to 0.70, cost 50, discount 0.92, retention 0.40); capacities 0.55 and 0.85 and retention 0.60 and 0.80 are added for comparison.

Calculated values

T0
162.00
T1
252.00
Annual gain
90.00
Present value
248.976
Net of cost
198.976
Officeholder benefit
36.00
Officeholder
Rejects

Hypothetical teaching numbers, not historical data. Raising collection capacity from 0.45 to 0.70 lifts revenue from 162.00 to 252.00, a gain of 90.00 a year worth 90.00 x 2.7664 = 248.976 over three years, so the project is valuable at a cost of 50. The officeholder counts only 0.40 x 90.00 = 36.00, so it rejects the project; it would need a retention probability of at least 50 / 90.00 = 0.556.

Worked steps

  1. T0 = 0.45 x 0.18 x 2,000 = 162.00
  2. T1 = 0.70 x 0.18 x 2,000 = 252.00; gain 252.00 - 162.00 = 90.00
  3. PV = 90.00 x (1 + 0.92 + 0.8464) = 90.00 x 2.7664 = 248.976
  4. Net = 248.976 - 50 = 198.976
  5. Officeholder: 0.40 x 90.00 = 36.00 against 50, so it rejects the project
  6. Break-even retention = 50 / 90.00 = 0.556

Use the idea

When state capacity stays low, compare the project's present value with the decision maker's expected private share.

Where the conclusion applies

A fixed base and rate, a three-year horizon for the social value and an officeholder who values only next year's gain; compliance and privacy costs are omitted, as in the book.

Check your understanding: At p = 0.60, does the officeholder invest?
0.60 x 90 = 54 > 50, so it invests; the break-even probability is 50/90 = 0.556.

Chapter 79 source: section "Fiscal Capacity & State Building".