The Encyclopedia of Economic Principals

Chapter 64

Institutions, State Formation, and Long-Run Development

Commitment, credit and compounding behind long-run divergence.

Four of the chapter's worked examples, made interactive: a merchant boycott that disciplines a ruler, taxes that carry war debt, a growth gap that reverses an income lead, and catch-up from far behind. All numbers are the chapter's constructed teaching numbers, not historical data.

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

When can merchants discipline a ruler?

How much commerce must merchants withdraw to make confiscation a losing move?

The ruler compares a stream of protected revenue with a one-time grab plus whatever commerce survives the boycott. Only a boycott broad enough to remove more than m* of future commerce makes the grab a loss. A more patient ruler values the stream more, so a smaller boycott suffices.

Equation, written in LaTeX: V_H=\frac{24-6}{1-0.75}=72.

Equation, written in LaTeX: m\geq\frac{55}{72}\approx0.764.

Equation, written in LaTeX: V_P(0.25)=55+72(0.75)=109,

Scroll sideways for the whole equation

Protected commerce yields revenue T = 24 a year at protection cost c = 6. delta is the ruler's discount factor and V_H the value of protecting forever. Confiscation pays 55 once; m is the share of future commerce merchants withdraw afterwards, and V_P(m) is the value of confiscating.

Predict first. If only a quarter of the merchants boycott, does the ruler respect property?

Your prediction

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Figure: When can merchants discipline a ruler? Two bars: protecting is worth 72.00 and confiscating with 1.000 of commerce withdrawn is worth 55.00. The threshold share is 0.764.
Share of commerce withdrawn: 1, Ruler's discount factor: 0.75
Constructed example: constructed teaching numbers, not historical data. The book's invented values are T = 24, c = 6, delta 0.75, payoff 55 and shares 0.25, 0.764 and 1; a share of 0.50 and discount factors 0.60 and 0.90 are added.

Calculated values

Cooperate value V_H
72.00
Confiscate value V_P(m)
55.00
Threshold share m*
0.764
Share withdrawn m
1.000
Ruler's choice
Protect

Constructed teaching numbers, not historical data. Cooperation is worth (24 - 6) / (1 - 0.75) = 72.00. Withdrawing 1.000 of commerce leaves the ruler 55 + 0.00 = 55.00 from confiscation, so protection pays and the ruler respects property. Deterrence needs m at least 55 / 72.00 = 0.764.

Worked steps

  1. V_H = (24 - 6) / (1 - 0.75) = 18 / 0.25 = 72.00
  2. Commerce kept after confiscation: (1 - 1.000) x 72.00 = 0.00
  3. V_P(m) = 55 + 0.00 = 55.00
  4. m* = 55 / 72.00 = 0.764
  5. V_P(m) = 55.00 against V_H = 72.00: protection pays and the ruler respects property

Use the idea

To judge whether a collective sanction is credible, compare the one-time gain from breaking a promise with the share of future business the sanction actually removes.

Where the conclusion applies

Constant revenue and cost, an infinite horizon, and a boycott that merchants enforce on their own members. The chapter's merchant side (12 > 9) shows members comply under its assumed sanction.

Check your understanding: What is the ruler's payoff from confiscation when m = 0.25 and delta = 0.75?
55 + 72 x 0.75 = 109, above 72, so confiscation pays.

Chapter 64 source: section "Merchant-guild commitment mechanism".

Demonstration 2 of 4

Taxes that let a state borrow for war

How does a continuing tax change wartime borrowing and later repayment?

Interest on inherited debt plus spending minus taxes is the new borrowing. A continuing tax lowers wartime borrowing one for one and, once military spending falls, leaves a primary surplus that can exceed interest, so debt shrinks.

Equation, written in LaTeX: D_{t+1}=1.05(240)+60+90-120=282.

Equation, written in LaTeX: D_{t+2}=1.05(282)+60+35-120=271.10.

Equation, written in LaTeX: D_{t+1}=1.05(240)+60+90-95=307.

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D is public debt, r the interest rate, G = 60 civilian spending, M military spending (90 in war, 35 in peace) and T tax revenue. Debt evolves as D_t+1 = (1 + r) D_t + G + M - T.

Predict first. Without the new excise (taxes 95), how much more must the state borrow in the war year?

Your prediction

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Figure: Taxes that let a state borrow for war. Three debt bars: 240 at the start, 282.00 after the war year and 271.10 after the peace year, with taxes of 120 and interest at 5%.
Tax revenue: 120, Interest rate: 5%
Constructed example: constructed teaching numbers, not historical data. The book's invented values are D = 240, r = 0.05, G = 60, M = 90 and 35, and taxes 95 or 120; taxes of 145 and rates of 3 and 8 percent are added.

Calculated values

War year debt D_t+1
282.00
War borrowing
42.00
Peace year debt D_t+2
271.10
Peace primary surplus
25.00
Peace interest
14.10
Peace change in debt
-10.90

Constructed teaching numbers, not historical data. With taxes of 120 and interest at 5%, war-year debt is 1.05 x 240 + 60 + 90 - 120 = 282.00, so the state borrows 42.00. In the peace year the primary surplus is 25.00 against interest of 14.10, so debt falls by 10.90.

Worked steps

  1. D_t+1 = 1.05 x 240 + 60 + 90 - 120 = 252.00 + 150 - 120 = 282.00
  2. War borrowing = 282.00 - 240 = 42.00
  3. D_t+2 = 1.05 x 282.00 + 60 + 35 - 120 = 296.10 + 95 - 120 = 271.10
  4. Primary surplus = 120 - 60 - 35 = 25.00; interest = 0.05 x 282.00 = 14.10
  5. Change in peace = 14.10 - 25.00 = -10.90, so debt falls by 10.90

Use the idea

Judge whether a debt is sustainable by comparing the peacetime primary surplus with interest on the debt, not by the size of the debt alone.

Where the conclusion applies

One-year debt, a fixed interest rate and no inflation, collection cost or maturity structure, as the chapter states.

Check your understanding: In the peace year with taxes 120 and r = 0.05, why does debt fall by 10.90?
The primary surplus is 120 - 60 - 35 = 25 and interest is 0.05 x 282 = 14.10; 25 - 14.10 = 10.90.

Chapter 64 source: section "Fiscal-military state".

Demonstration 3 of 4

Rich colonies that fell behind

Can a small persistent growth gap reverse a fifty percent income lead?

A steeper link from initial prosperity to extractive institutions widens the growth gap. Compounding turns that gap into a reversal only if the horizon is long enough.

Equation, written in LaTeX: J=1-0.60P.

Equation, written in LaTeX: g=0.008+0.025J.

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P is an invented initial prosperity index (0.90 for A, 0.30 for B), J an invented institutional inclusion index and g annual growth. Income starts at 150 in A and 100 in B and compounds yearly.

Predict first. A starts fifty percent richer. Is it still ahead after 60 years at the book's slope 0.60?

Your prediction

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Figure: Rich colonies that fell behind. Left: income paths over 60 years, A from 150 to 477.89 and B from 100 to 539.83. Right: the ratio of A to B income, ending at 0.8853.
Slope of inclusion on prosperity: 0.6, Horizon (years): 60
Constructed example: constructed teaching numbers, not historical data. The book's invented values are P = 0.90 and 0.30, slope 0.60, incomes 150 and 100 and 60 years; slopes 0.30 and 0.90 and horizons 20 and 40 years are added.

Calculated values

J_A
0.460
J_B
0.820
g_A
1.950%
g_B
2.850%
Y_A
477.89
Y_B
539.83
Ratio Y_A / Y_B
0.8853

Constructed teaching numbers, not historical data. With slope 0.60, inclusion is 0.460 in A and 0.820 in B, so A grows 0.008 + 0.025 x 0.460 = 0.01950 a year and B 0.008 + 0.025 x 0.820 = 0.02850. After 60 years income is 477.89 in A and 539.83 in B: B has overtaken A, which is 11.5% poorer.

Worked steps

  1. J_A = 1 - 0.60 x 0.90 = 0.460; J_B = 1 - 0.60 x 0.30 = 0.820
  2. g_A = 0.008 + 0.025 x 0.460 = 0.01950; g_B = 0.008 + 0.025 x 0.820 = 0.02850
  3. Y_A = 150 x (1.01950)^60 = 477.89
  4. Y_B = 100 x (1.02850)^60 = 539.83
  5. Y_A / Y_B = 477.89 / 539.83 = 0.8853

Use the idea

When comparing places over long periods, ask how big a persistent growth difference must be to overturn an initial lead, and how long it takes.

Where the conclusion applies

Every index, equation, rate and horizon is invented by the chapter for teaching and estimates nothing about actual colonies.

Check your understanding: At slope 0.60, after 40 years, which colony is richer?
150 x 1.0195^40 = 324.77 against 100 x 1.0285^40 = 307.73, so A is still ahead.

Chapter 64 source: section "Reversal of fortune".

Demonstration 4 of 4

Catching up from far behind

Why does the same catch-up share give faster growth to the economy further behind?

Closing a fixed share of a larger gap adds more productivity on a smaller base, so percentage growth is far higher for the latecomer. Financing the adoption is a separate question, settled by the package's present value against its cost.

Equation, written in LaTeX: A_1=35+0.25(100-35)=51.25.

Equation, written in LaTeX: A_1=75+0.25(100-75)=81.25,

Equation, written in LaTeX: PV=20(\frac{1-(1.08)^{-5}}{0.08})\approx79.85.

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A* = 100 is frontier productivity, A_0 the latecomer's starting productivity and theta the share of the gap it closes in one period. PV values an adoption package paying 20 a year for 5 years at 8 percent.

Predict first. With the same catch-up share 0.25, who grows faster in percent, the economy at 35 or the one at 75?

Your prediction

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Figure: Catching up from far behind. Two bars against a frontier line at 100: productivity 35 before and 51.25 after, growth 46.43%.
Starting productivity: 35, Share of gap closed: 0.25
Constructed example: constructed teaching numbers, not historical data. The book's invented values are frontier 100, starting levels 35 and 75, share 0.25 and the 72 package paying 20 for 5 years at 8 percent; a starting level of 55 and shares 0.10 and 0.40 are added.

Calculated values

A_1
51.25
Growth
46.43%
Gap closed
16.25
Package PV
79.85
Package NPV
7.85

Constructed teaching numbers, not historical data. Starting at 35 with a gap of 65, closing 25% of it lifts productivity to 35 + 0.25 x 65 = 51.25, growth of 46.43%. The larger the starting gap, the faster the percentage growth from the same catch-up share. The book's adoption package, a fixed example, is worth 79.85 against its cost of 72, an NPV of 7.85.

Worked steps

  1. Gap = 100 - 35 = 65
  2. A_1 = 35 + 0.25 x 65 = 35 + 16.25 = 51.25
  3. Growth = (51.25 - 35) / 35 = 0.4643, or 46.43%
  4. PV = 20 x (1 - 1.08^-5) / 0.08 = 79.85; NPV = 79.85 - 72 = 7.85

Use the idea

Read fast growth in a poor economy partly as the arithmetic of a large gap, and test any adoption package by its net present value, not by whether it can be financed.

Where the conclusion applies

A fixed frontier for one period and a catch-up share independent of the gap; in the chapter the share depends on institutions that can absorb and finance adoption.

Check your understanding: With starting productivity 75 and share 0.25, what is growth?
A_1 = 75 + 0.25 x 25 = 81.25, so growth is 81.25 / 75 - 1 = 8.33 percent.

Chapter 64 source: section "Advantage of backwardness".