The Encyclopedia of Economic Principals

Chapter 65

Economic History, Trade, Technology, and Divergence

Price a machine, balance a land budget, test an enforcement chain and measure a counterfactual.

Four of the chapter's invented teaching calculations, made interactive: one machine priced in two regions, coal and imports against a land limit, collective liability for merchants, and railroad social savings. All numbers are constructed teaching numbers, not historical data. The slave-trade persistence example stays in the text.

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

Same machine, different regions

Does one machine design pay everywhere, or only where labor is dear and energy cheap?

The machine trades labor for energy. Its gain rises with the wage and falls with the energy price, so the same design crosses the zero NPV line in one price setting and not in another.

Equation, written in LaTeX: A_5=\frac{1-(1.08)^{-5}}{0.08}\approx3.992710.

Equation, written in LaTeX: G_H=11(720)-0.80(600)-480=6{,}960.

Equation, written in LaTeX: NPV_L=1{,}680(3.992710)-9{,}600\approx-2{,}892.25.

Equation, written in LaTeX: w^*=\frac{9{,}600/3.992710+0.80(600)+480}{720}\approx4.67.

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The machine costs F = $9,600, saves 720 labor hours a year, uses 600 energy units and $480 of maintenance, lasts five years and is discounted at 8 percent. w is the hourly wage, p_e the energy price, G the annual gain and A_5 the annuity factor.

Predict first. Is the machine profitable where labor is cheap ($4.50) and energy dear ($1.80)?

Your prediction

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Figure: Same machine, different regions. Net present value of the same machine against the hourly wage for three energy prices. At wage 11 and energy price 0.80 the NPV is 18,189.26; the break-even wage is 4.67.
Hourly wage ($): $11, Energy price ($ per unit): $0.80
Constructed example: constructed teaching numbers, not historical data. The book's invented machine with region H (wage 11, energy 0.80) and region L (wage 4.50, energy 1.80); the wage 6 and energy price 1.30 are added for comparison.

Calculated values

Annuity factor A_5
3.992710
Annual gain G
$6,960.00
Present value
$27,789.26
Net present value
$18,189.26
Break-even wage
$4.67
Decision
Adopt

At a wage of $11.00 and an energy price of $0.80, the annual gain is 11 x 720 - 0.80 x 600 - 480 = 6,960.00, worth $27,789.26 over five years at 8 percent, so NPV = 27,789.26 - 9,600 = 18,189.26: the machine pays. The wage must exceed $4.67 at this energy price. Constructed teaching numbers, not historical data.

Worked steps

  1. A_5 = (1 - 1.08^-5) / 0.08 = 3.992710
  2. G = 11 x 720 - 0.80 x 600 - 480 = 7,920.00 - 480.00 - 480 = 6,960.00
  3. PV = 6,960.00 x 3.992710 = 27,789.26
  4. NPV = 27,789.26 - 9,600 = 18,189.26
  5. w* = (9,600 / 3.992710 + 480.00 + 480) / 720 = 4.67

Use the idea

Price one fixed design under each location's wage and energy cost before asking why adoption differed.

Where the conclusion applies

Constant annual gain, a known life and discount rate, full-cost wages and energy priced at the point of use. Credit limits or unreliable machines can block a positive NPV.

Check your understanding: At w = 4.50 and p_e = 1.80, what is NPV?
G = 3,240 - 1,080 - 480 = 1,680; NPV = 1,680 x 3.992710 - 9,600 = -2,892.25.

Chapter 65 source: section "High-wage, cheap-energy mechanization".

Demonstration 2 of 4

Coal plus colonies relax the land limit

Can coal, imports, or only both together let a region outgrow its land?

Each relief channel subtracts land-equivalents from the gross need. The proposed scale fits only when the net requirement falls to the local land line.

Equation, written in LaTeX: D_0=98+62=160,

Equation, written in LaTeX: D_1=98+62-14-11=135.

Equation, written in LaTeX: D_C=160-14=146,

Equation, written in LaTeX: D_X=160-11=149,

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F = 98 is land for food and fiber and B = 62 the land equivalent of biomass energy. C is the land displaced by coal, X the land embodied in imports, D the net local requirement and L-bar the local land.

Predict first. With 140 units of land, is either coal or imports alone enough?

Your prediction

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Figure: Coal plus colonies relax the land limit. Bars for gross land need 160, relief 25 and net need 135, with local land at 140.
Coal substitution: 14, Imported land-equivalents: 11, Local land: 140
Constructed example: constructed teaching numbers, not historical data. The book's invented region (land 140, needs 98 and 62, coal 14, imports 11); land of 130 and 150 is added for comparison.

Calculated values

Gross requirement F + B
160
Relief C + X
25
Net requirement D
135
Local land
140
Balance
Slack 5

Gross need is 98 + 62 = 160 land units. Coal relief 14 and imports 11 cut it to 160 - 25 = 135, against 140 units of local land: slack 5, so the scale fits. Constructed teaching numbers, not historical data.

Worked steps

  1. F + B = 98 + 62 = 160
  2. R = C + X = 14 + 11 = 25
  3. D = 160 - 25 = 135
  4. 140 - 135 = 5, so slack 5

Use the idea

Build a dated land-equivalent account, test each relief channel separately, then together, and report ranges for the conversion factors.

Where the conclusion applies

Land-equivalent accounting with fixed conversion factors. It does not make coal, grain and cotton physically interchangeable, and imported relief can shift costs onto other places.

Check your understanding: With coal only, what is the deficit?
160 - 14 = 146; 146 - 140 = 6.

Chapter 65 source: section "Great Divergence coal-and-colonies hypothesis".

Demonstration 3 of 4

Holding the whole community liable

When does collective liability make a distant merchant keep his word?

Two inequalities must hold: the fine must exceed the gain from default, and enforcing must cost the community less than the outside sanction for refusing.

Equation, written in LaTeX: 0.15(40)=6,

Equation, written in LaTeX: 18-6=12>0.

Equation, written in LaTeX: U_D=18-24=-6,

Equation, written in LaTeX: 9<60,

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g = 18 is the gain from default. The private remedy recovers with probability 0.15 and penalty 40. The home community can fine f = 24 at cost k = 9; refusing redress exposes its members to an outside sanction S.

Predict first. If foreign authorities can impose only 7, will the community punish its cheater?

Your prediction

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Figure: Holding the whole community liable. Left: merchant's gain 18, the community fine 24 and the default payoff -6. Right: community enforcement cost 9 against outside sanction 60.
Enforcement regime: Community responsibility, Outside sanction on the community: 60
Constructed example: constructed teaching numbers, not historical data. The book's invented merchant (gain 18, recovery 0.15 and 40, fine 24, cost 9, sanctions 60 and 7); a sanction of 30 is added for comparison.

Calculated values

Expected private cost
6
Default payoff, private remedy
12
Default payoff if the fine is applied
-6
Community enforces
Yes
Outcome
Performance: the fine deters

The community fine turns default into 18 - 24 = -6, and k = 9 < S = 60, so the community enforces: the threat is credible and the merchant performs. Constructed teaching numbers, not historical data.

Worked steps

  1. 0.15 x 40 = 6
  2. Private remedy: 18 - 6 = 12 > 0
  3. Community fine: U_D = 18 - 24 = -6
  4. Credibility: k = 9 versus S = 60: 9 <= 60

Use the idea

Check both stages separately: the individual's payoff from cheating and the intermediary's cost of disciplining versus the loss it faces if it does not.

Where the conclusion applies

Accurate verification of complaints and observable membership. Collective liability also punishes innocent members and can harden communal boundaries.

Check your understanding: Under the private remedy, what is the expected payoff from defaulting?
18 - 0.15(40) = 18 - 6 = 12.

Chapter 65 source: section "Community responsibility system".

Demonstration 4 of 4

Measuring what railroads saved

How much did rail save compared with a feasible canal-and-road system?

Traffic that moves under both systems saves the full cost gap. Traffic that moves only at the rail price is worth less than the gap to its users, a triangle under linear demand.

Equation, written in LaTeX: c_C-c_R=0.07-0.04=0.03.

Equation, written in LaTeX: 0.03(7{,}000{,}000)=210{,}000.

Equation, written in LaTeX: \frac{1}{2}(0.03)(10{,}000{,}000-7{,}000{,}000)=45{,}000.

Equation, written in LaTeX: SS_0=0.03(10{,}000{,}000)=300{,}000.

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c_R = 0.04 is rail cost per ton-mile and Q_R = 10 million ton-miles rail traffic. c_C is the canal-and-road cost and Q_C the traffic that would move at that cost. SS is social savings and SS_0 the fixed-demand version.

Predict first. Does assuming all rail traffic would have moved anyway overstate or understate the savings?

Your prediction

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Figure: Measuring what railroads saved. Transport cost lines at 0.07 and 0.04 with the saving on 7 million retained ton-miles shaded, plus the induced-traffic triangle up to 10 million. Social savings 255,000.
Canal-and-road cost per ton-mile ($): 0.07, Traffic under the alternative (million ton-miles): 7
Constructed example: constructed teaching numbers, not historical data. The book's invented freight case (rail 0.04 and 10 million, alternative 0.07 and 7 million, fixed-demand 10 million); costs 0.05 and 0.10 and traffic of 5 million are added for comparison.

Calculated values

Cost gap
0.03
Rectangle
210,000
Triangle
45,000
Social savings
255,000
Fixed-demand estimate
300,000
Overstatement
45,000

With an alternative cost of 0.07 and 7 million ton-miles under it, social savings are 210,000 + 45,000 = 255,000. Holding all rail traffic fixed overstates the savings by 45,000. Constructed teaching numbers, not historical data.

Worked steps

  1. c_C - c_R = 0.07 - 0.04 = 0.03
  2. Rectangle = 0.03 x 7,000,000 = 210,000
  3. Triangle = 0.5 x 0.03 x (10,000,000 - 7,000,000) = 45,000
  4. SS = 210,000 + 45,000 = 255,000
  5. SS_0 = 0.03 x 10,000,000 = 300,000; overstatement 45,000

Use the idea

Name the alternative network first, then report savings from fixed demand down through several demand responses.

Where the conclusion applies

Constant transport costs, linear demand and a static one-period comparison with no settlement or innovation effects.

Check your understanding: What is the overstatement of the fixed-demand estimate?
300,000 - 255,000 = 45,000.

Chapter 65 source: section "Railroad social savings".