A Theory of Contract Choice and the California Gold Rush - Exhaustive Study Notes

Introduction to the Theory of Contract Choice and the California Gold Rush

• General Premise of Exchange and Contracts

  • John Umbeck posits that every exchange between two or more people involves a contract, whether it is explicit or implicit.

  • Contracts can take numerous forms depending on the discretion of the contracting parties.

  • The paper utilizes the tools of price theory—specifically a model developed by Steven N. S. Cheung—to explain the choice of contracts observed among miners during the California gold rush (1848–1850).

• Cheung’s 1969 Theory of Contract Choice

  • Cheung’s basic proposition is that individuals, when choosing between a fixed rent or a sharing contract, will select the one that minimizes risk (defined as variance in income), subject to the constraint of positive transaction costs.

• Umbeck’s Modifications to Cheung’s Model

  • There are three significant differences requiring modifications for the Gold Rush application:

    1. Delineation of Property Rights: Cheung assumes property rights to factors of production are already delineated. In the California gold fields, mineral lands were a nonexclusive resource; thus, the theory must account for the costs of privately maintaining exclusive rights.

    2. Production Technology: Cheung focused on agriculture. Umbeck argues that contracting costs are functions of both production technology and the nature of the good produced. The characteristics of gold and 1840s mining techniques must be examined.

    3. Income Variance vs. Contracting Costs: While Cheung tests changes in income variance across crops, Umbeck focuses on differences in contracting costs, assuming differences in income variance are of minor importance for the empirical work.

Theoretical Framework for Gold Mining Contracts

• The Scenario

  • Wealth-maximizing individuals are placed on a limited quantity of land containing gold.

  • Gold is distributed randomly and requires labor effort to acquire.

  • There is no government to assign ownership rights.

  • Individuals must agree on a contract—either a sharing contract or a land allotment contract—to avoid violent conflicts.

• The Sharing Contract

  • Miners agree not to compete for rights.

  • They claim a specific area from which non-group members are excluded.

  • Within the group, no individual can exclude another from any gold-bearing land.

  • Each member agrees to work a set number of hours per production period.

  • At the end of the period, all gold is pooled, measured, and divided according to a pre-agreed formula.

  • Violations of the agreement are punished by the group.

• The Land Allotment Contract

  • Miners claim a specific area but then allot a particular piece of that land to each member.

  • Each individual owner can exclude all other group and non-group members from their plot.

  • Each miner works their own land as much as they choose and keeps all the gold they find.

  • Violations (e.g., trespassing) are punished by the group.

Comparison of Contractual Costs

• Costs of Reaching Agreement (Initial Distribution)

  • Both contracts require negotiation to determine the initial distribution of wealth (gold portions or land size).

  • The costs of reaching this agreement are constrained by the threat of personal violence (the alternative to contract).

  • Assuming wealth maximization, these costs are generally comparable across both contract types.

• Costs of Measuring and Dividing the Product

  • Gold: Requires measurement only at the margin of weight. This is done with simple balances at trivial costs.

  • Land: If land is homogeneous, measurement is required only for square footage ($ft^2$).

  • Time Factor: Sharing contracts require measurement/division after every production period. Land allotment requires measurement only once at the beginning.

• Costs of Enforcement (Theft and Trespass)

  • External Enforcement: Costs to exclude outsiders are identical for both contracts.

  • Internal Enforcement (Land Allotment): Trespassing is easily determined by observing someone within the physical boundary markers of another’s plot.

  • Internal Enforcement (Sharing): Because gold is small and valuable (high value-to-bulk ratio), it is easy to conceal and avoid sharing. This makes sharing enforcement costs high.

• Costs of Enforcing Work Requirements

  • Under sharing contracts, the incentive to "shirk" (reduce labor input) is high. If a miner keeps only $50\%$ of their discovery, the cost of a day’s leisure is halved, increasing the demand for leisure.

  • Resources must be spent monitoring peers to ensure they fulfill work requirements. Monitoring costs depend on proximity; working a large area makes monitoring more expensive than a small area.

  • In land allotment, work enforcement costs are zero because the miner keeps $100\%$ of their find.

The Impact of Group Size on Contract Choice

• The Hypothesis

  • As group size ($N$) increases, the relative costs of the sharing contract rise compared to the land allotment contract.

  • Negotiation Costs: More people increase the difficulty of agreement.

  • Theft Incentive: In a group of 10, a miner loses $90\%$ of a find to the group. In a group of 100, they lose $99\%$. This increases the incentive to conceal gold.

  • Shirking Incentive: As $N$ increases, individual rewards for group effort decline, requiring more monitoring resources.

• The Gains from Sharing

  • The primary gain from sharing is the reduction of income variance.

  • If $N$ miners claim land $L$ with gold $G$, expected income is $\frac{G}{N}$.

  • As $N$ increases for a fixed quantity of land and gold ($2N$ miners), the expected income becomes $\frac{G}{2N}$, and the variance in income under a land allotment contract actually decreases.

  • Therefore, as group size increases, the relative gains of sharing decline while the costs rise.

• Testable Implication

  • There is an inverse relationship between the size of the contracting group and the observed frequency of sharing contracts.

Socio-Legal and Technological Constraints in California (1848-1850)

• Legal Context

  • Pre-1846: Mexican laws allowed land acquisition via petition and map.

  • 1846-1848: Military rule during the Mexican-American War.

  • Treaty of Guadalupe Hidalgo (Feb 2, 1848): Ended the war; property became US Federal land.

  • Jan 24, 1848: Gold discovered at the American River (Sutter’s Mill).

  • Colonel Mason’s Decree (Feb 12, 1848): Abolished Mexican mining laws but didn't replace them. Military force was insufficient to handle the "shouting" miners; soldiers deserted (from 1,059 to 660).

  • Gold lands were an unconstrained, nonexclusive resource.

• Technological Context (Placer Mining)

  • Gold was found in superficial placer deposits.

  • The Pan: Circular motion in water floats sand/dirt, leaving gold. Basis for all methods.

  • The Cradle (Rocker): Introduced early 1848. A box ($40\,inches \times 20\,inches \times 4\,inches$) on rockers. A "riddle box" with $\frac{1}{2}\,inch$ holes filters rocks. Two miners using a cradle could wash 300 pans a day (3x speed of one man).

  • The cradle required continuous motion; stopping caused sand to pack the cleats. This created a technological incentive for small partnerships (one digging/hauling, one rocking).

• Population Growth

  • May 1848: 800 miners.

  • June 1848: 2,000 miners.

  • July 1848: 4,000 miners.

  • End of 1848: 5,000 to 10,000 miners.

  • 1849: News spreads globally. 8,000 left NYC; 2,000 from Boston; 1,200 from New Orleans. Total by sea: 20,000 from the US East Coast. San Francisco Harbor Master reported 40,000 arrivals by boat.

  • End of 1849: 107,000 total miners.

  • 1852: 264,000 total miners.

Empirical Evidence from the Gold Fields

• Early 1848: The Dominance of Sharing

  • Small groups (2-8) used sharing contracts.

  • Gold was divided evenly, with one exception: nuggets weighing more than $\frac{1}{2}\,ounce$ found before reaching the cradle belonged to the discoverer.

  • Enforcement was easy because final extraction occurred only when cleaning the cradle cleats at the end of the day.

• River Bed Mining Projects (1849)

  • Projects involved digging ditches and building dams to divert rivers.

  • On the North Fork of the American River, nine separate groups (8-16 people each) built nine separate dams/ditches.

  • They did not merge into one large project because the enforcement costs of a sharing contract for a very large group exceeded the savings of building fewer dams (each dam cost approx. $\$8,000$).

• The Failure of Large Joint-Stock Companies

  • Over 120 groups formed on the East Coast/Midwest with approx. 50 members each, bound by equal-sharing contracts.

  • None survived more than one month in the mines.

  • Average daily yield for these large groups was $\$3.16$ per member, while individual or small-group yield was $\$12$ to $\$16$.

  • Failure was attributed to the inability to monitor work and discoveries in large groups.

• The Transition to Land Allotment (Summer 1849)

  • As populations surged, sharing contracts encountered systemic difficulties.

  • Wood’s Creek: Miners shifted from working "where it was richest" to using tape measures to divide ground into claims.

  • Middle Fork of the American River: 1,500 men originally worked on shares with daily assessments for the "drunk or absent." Dissatisfaction led to breaking into 15-foot wide claims.

  • Nevada City: Ravines were originally exclusive to the first party; as population rose, rules were established for 30-foot square claims.

• Establishment of Mining Districts

  • Over 500 districts were formed (population 4 to 8,000).

  • Umbeck found records for nearly 200 districts; sharing arrangements did not survive after 1850.

  • Example: Jackass Gulch (1849) Contract Provisions:

    1. Individual may hold one claim by virtue of occupation ($\leq 100\,feet$ square).

    2. Purchased claims require a bill of sale and certification by two disinterested persons.

    3. A jury of 5 persons decides disputes.

    4. Notices must be posted and renewed every 10 days.

    5. Forfeiture of property after 5 days of absence (except for sickness/accident).

    6. Defined geographic boundaries (Jackass and Soldier gulches).

Conclusions

• The Role of Transaction Costs: Economic theory requires an understanding of transaction costs to explain the existence of contracts, firms, and nonexclusive property.

• Contract Choice as a Proxy: Investigating contract forms yields insight into variables affecting the costs of exchange.

• Evolution of Local Law: The land allotment system worked so efficiently that the US Federal Government eventually adopted it into the mining statutes of 1866.

• Future Research: The circularity between laws, governmental institutions, and transaction costs requires further specification to find a general equilibrium solution for contract choice.