The Encyclopedia of Economic Principals

Chapter 75

Institutional Persistence, Path Dependence, and Evolution

Why institutions spread, stick, and provoke resistance.

Four of the chapter's worked examples, made interactive: search and selection among workshop routines, legitimacy as a substitute for enforcement, the horizon that locks in an old system, and the threshold at which a broken allocation rule sparks collective action. 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

Search, imitation, and selection among routines

How much of a productivity gain comes from firms finding better routines, and how much from better routines gaining market share?

Search changes which routines exist; selection changes how much of the market each routine serves. The defective variant shows that search is not automatic improvement. With equal shares the average would stay at 10.17; the weighted average rises because the productive routine grows and the failure leaves.

Equation, written in LaTeX: \bar A_0=\frac{9(9)+3(13)}{12}=10.

Equation, written in LaTeX: \bar A_1=\frac{7(9)+4(13)+1(7)}{12}=\frac{122}{12}\approx10.17.

Equation, written in LaTeX: \bar A_2=\frac{7(9)+8(13)}{15}=\frac{167}{15}\approx11.13.

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Each bar is one repair workshop. Routine O completes 9 jobs per worker-week, routine N 13 and the defective variant D 7. The average is weighted by market weight: equal shares before selection, then weight 1 for O, the chosen weight for N and 0 for D, which exits.

Predict first. Does most of the rise from 10 to 11.13 come from the workshop that copies N, or from N workshops expanding while D exits?

Your prediction

Choose an example

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Figure: Search, imitation, and selection among routines. Bars for each workshop at the stage after selection, height equal to jobs per worker-week and width equal to market weight. The average productivity line sits at 11.13.
Stage: After selection, Expansion weight on N workshops: 2
Constructed example: the chapter's hypothetical twelve workshops (9, 13 and 7 jobs, expansion weight 2 for N); expansion weights 1 and 3 are added for comparison.

Calculated values

Stage
After selection
Weighted total
167
Total weight
15
Average productivity
11.13
Change from initial 10
1.13

With N workshops expanding at weight 2 and D exiting, the average is 167 / 15 = 11.13. Of the 1.1333 rise from 10, search supplies 0.1667 and selection 0.9667, so most of the gain comes from reweighting and exit rather than from the new adopter.

Worked steps

  1. Weights: O 1 each, N 2 each, D exits (weight 0)
  2. Weighted total = 7 x 9 + 4 x 2 x 13 = 63 + 104 = 167
  3. Total weight = 7 + 4 x 2 = 15
  4. Average = 167 / 15 = 11.1333, about 11.13
  5. Search gain 10.1667 - 10 = 0.1667; selection gain 11.1333 - 10.1667 = 0.9667

Use the idea

When average productivity in an industry rises, split the change into firms improving and market share moving toward firms that were already better before crediting either.

Where the conclusion applies

Twelve workshops, fixed productivity per routine, and expansion weights imposed rather than derived from prices. The weights 1 and 3 are added for comparison.

Check your understanding: If every workshop kept an equal share after search, what would average productivity be?
7 x 9 + 4 x 13 + 1 x 7 = 122, and 122 / 12 = 10.17. Selection at weight 2 then lifts it to 167 / 15 = 11.13, so 0.9667 of the 1.1333 gain comes from selection.

Chapter 75 source: section "Evolutionary routines".

Demonstration 2 of 4

Legitimacy lowers the cost of compliance

How much enforcement does an authority save when riders accept its rules as legitimate?

Each point of legitimacy adds 0.025 to compliance for free, so less paid enforcement is needed to reach the same target. The vertical distance between the lines is the compliance that legitimacy supplies; the target line shows how much effort must fill the rest.

Equation, written in LaTeX: c=0.42+0.025L+0.06e,

Equation, written in LaTeX: e_A=\frac{0.84-0.42-0.025(8)}{0.06}=\frac{0.22}{0.06}\approx3.67.

Equation, written in LaTeX: 3(\$150{,}000)-\$180{,}000=\$270{,}000.

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c is the share of riders who follow the rationing rule, L the legitimacy stock (0 to 10) and e enforcement effort, each unit costing $90,000. Penalties, travel alternatives and the directive itself are held fixed, so differences in cost are attributed to L.

Predict first. How much annual enforcement does raising L from 2 to 6 save at 84 percent required compliance?

Your prediction

Choose an example

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Figure: Legitimacy lowers the cost of compliance. Compliance rises linearly with enforcement effort, one line per legitimacy stock. The line for L = 2 meets the required compliance 0.84 at effort 6.17.
Legitimacy stock L: 2, Required compliance: 84%
Constructed example: the chapter's hypothetical transit authorities (L = 8, 2 and 6, 84 percent compliance, $90,000 per effort unit, $180,000 reform); L = 4 and compliance targets of 76 and 92 percent are added for comparison.

Calculated values

Required effort e
6.17
Annual enforcement cost
$555,000
Effort at L = 2
6.17
Annual saving vs L = 2
$0
Three-year saving minus $180,000 reform
-$180,000

To reach 0.84 compliance with L = 2, effort must cover 0.84 - 0.42 - 0.025 x 2 = 0.37, so e = 0.37 / 0.06 = 6.17 and the annual cost is $555,000. At the baseline stock L = 2 there is no saving, so a $180,000 reform that left L at 2 would be a pure loss of $180,000.

Worked steps

  1. e = (0.84 - 0.42 - 0.025 x 2) / 0.06 = 0.37 / 0.06 = 6.1667
  2. Cost = 0.37 x 90,000 / 0.06 = $555,000
  3. At L = 2: e = 0.37 / 0.06 = 6.1667, cost $555,000
  4. Saving = $555,000 - $555,000 = $0 per year
  5. Three years: 3 x $0 - $180,000 = -$180,000

Use the idea

When comparing reform spending with enforcement budgets, estimate how much a credible change in accepted authority lowers the effort needed for the same compliance.

Where the conclusion applies

A linear compliance rule, a stock that holds for three years after reform, and no discounting. If the reform works through more generous refunds, the saving mixes legitimacy with material incentive.

Check your understanding: Over three years, is a $180,000 reform that lifts L from 2 to 6 worth it, ignoring discounting?
e = (0.84 - 0.42 - 0.15) / 0.06 = 4.5, costing $405,000; the saving is $150,000 a year, and 3 x $150,000 - $180,000 = $270,000, so yes.

Chapter 75 source: section "Legitimacy as Political Capital".

Demonstration 3 of 4

Switching costs and horizon in lock-in

When does a better court filing system fail to replace an older one?

A better system can lose to an incumbent when the decision maker counts only a few years of gains against an up-front conversion cost. Lengthening the horizon or cutting the conversion cost through compatibility both reverse the choice without changing B itself.

Equation, written in LaTeX: \Delta b=18{,}000(\$11-\$7)+(\$90{,}000-\$55{,}000)=\$107{,}000.

Equation, written in LaTeX: PV_3=\$107{,}000(\frac{1-(1.05)^{-3}}{0.05})\approx\$291{,}388.

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The annual social gain from system B is $107,000. F is the one-time conversion cost, the discount rate is 5 percent and the horizon is how many years the decision maker counts.

Predict first. With the $320,000 conversion cost, does a four-year horizon reverse the decision to keep A?

Your prediction

Choose an example

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Figure: Switching costs and horizon in lock-in. Bars show the present value of the annual gain over horizons of 1 to 3 years against a line at the conversion cost $320,000. At 3 years the value is $291,388.
Decision horizon (years): 3, Conversion cost: $320,000
Constructed example: the chapter's hypothetical court network ($107,000 gain, 5 percent, conversion cost $320,000 or $180,000, horizons 2 to 4 years); a five-year horizon and a $250,000 cost are added for comparison.

Calculated values

Annual gain
$107,000
Annuity factor
2.723248
PV over 3 years
$291,388
Conversion cost F
$320,000
PV minus F
-$28,612
Decision
Retain A

Over 3 years at 5 percent, the $107,000 annual gain is worth 107,000 x 2.723248 = 291,388 dollars, which is below the $320,000 conversion cost, so a decision maker with this horizon rationally retains A. The system is the same in every case; only the horizon and the cost of conversion change.

Worked steps

  1. Gain = 18,000 x (11 - 7) + (90,000 - 55,000) = 72,000 + 35,000 = $107,000
  2. Factor = (1 - 1.05^-3) / 0.05 = 2.723248
  3. PV = 107,000 x 2.723248 = $291,388
  4. $291,388 < $320,000: retain A

Use the idea

Before calling a retained institution inefficient, compare the present value of switching over the decision maker's real horizon with the full conversion cost.

Where the conclusion applies

A constant annual gain, a 5 percent discount rate and no political opposition. A subsidy that only reimburses the cost changes the agency's threshold but not the social conversion cost.

Check your understanding: With a compatibility standard cutting F to $180,000, is a two-year horizon enough?
PV_2 = 107,000 x (1 - 1.05^-2) / 0.05 = 107,000 x 1.859410 = $198,957, above $180,000, so switch.

Chapter 75 source: section "Path Dependence and Institutional Lock-In".

Demonstration 4 of 4

Moral economy and the mobilization threshold

Why does the same shortage provoke protest in one town and not in another?

The shortage is the same in every scenario; what moves willingness to act is whether the accepted allocation rule was broken. Once the threshold is crossed, concession becomes the merchant's cheaper option.

Equation, written in LaTeX: 45>36

Equation, written in LaTeX: 0.60(\$3{,}200)+\$500=\$2{,}420.

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Residents act together only when the number willing to act exceeds the coordination threshold of 36. The merchant compares expected defiance cost (probability of disruption times its $3,200 cost, plus $500 of reputational loss) with the $900 cost of conceding.

Predict first. Under secret diversion, does the merchant still concede when disruption has probability 0.30?

Your prediction

Choose an example

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Figure: Moral economy and the mobilization threshold. Left: 45 residents willing to act against a threshold of 36. Right: expected defiance cost $2,420 against a concession cost of $900.
Scenario: B secret diversion, Probability of disruption: 0.6
Constructed example: the chapter's hypothetical town (threshold 36; 22, 45 and 25 willing; $3,200 disruption at probability 0.60, $500 reputation, $900 concession); disruption probabilities 0.30 and 0.90 are added for comparison.

Calculated values

Willing to act
45
Threshold
36
Mobilization
yes
Expected defiance cost
$2,420
Concession cost
$900
Merchant's response
concede

In scenario B, 45 residents are willing to act against a threshold of 36, so coordinated action is feasible. Facing disruption with probability 0.60, the merchant's expected defiance cost is 0.60 x 3,200 + 500 = 2,420 dollars, above the $900 cost of returning the 18 sacks under supervision, so the merchant concedes.

Worked steps

  1. Willing 45 > threshold 36: mobilize
  2. Expected defiance cost = 0.60 x 3,200 + 500 = 1,920 + 500 = $2,420
  3. Concession cost $900 < $2,420

Use the idea

When predicting protest over a scarce good, ask whether the allocation breaks a rule people already accept, not only how large the shortage is.

Where the conclusion applies

A fixed threshold, willingness counts taken from the chapter's scenarios and a risk-neutral merchant. The comparison explains the merchant's response, not social welfare.

Check your understanding: What is the expected defiance cost at a disruption probability of 0.30?
0.30 x 3,200 + 500 = $1,460, still above the $900 concession cost (the 0.30 probability is constructed).

Chapter 75 source: section "Moral economy".