Lecture 4: Smart Contracts as a Solution to a Coordination Problem
MIT OpenCourseWare
Adding time and risk to the model 0:00
This lecture builds on the earlier framework by adding contracting on top of information sharing, using distributed ledgers and multi-agent smart contracts. The setting now includes commodities indexed by time and by the history of nature's random draws, such as rainfall, alongside the earlier locations and states. Agents care about discounted expected utility, summing enjoyment over time and averaging over possible future states, and the underlying planning problem becomes a Lagrangian in which shadow prices attach to resource constraints for every date and history.
The mutual insurance result 7:35
Solving the planning problem gives a striking result: each person's consumption depends only on total, aggregate income, not on their own individual harvest. The intuition is a community rice pool, where everyone contributes their harvest and then receives a share back depending on the total available, so individual luck washes out once the pool is formed. A second implication is that consumption levels should move together across people, never crossing paths, even though some people consume more than others.
Testing smoothness in Indian villages 10:30
Ten years of data from villages in India, gathered by the ICRISAT crops institute, let Townsend check this prediction. Household incomes bounce around erratically and depend heavily on whether someone is a landless laborer or a large landholder, but grain consumption stays remarkably flat and level across households. Roughly speaking, only about seven cents of every extra dollar of income shows up in extra consumption, meaning households are absorbing most income shocks rather than passing them through to what they eat, though the fraction varies by activity, reaching close to a quarter for income from trade and handicrafts.
Why this surprised policymakers 14:30
The closeness of village households to the theoretical benchmark stunned policymakers, who assumed that a poor village divided by caste, with Brahmins and untouchables, could not possibly be smoothing consumption this well internally. Yet the data show that gifts, transfers, and grain storage within the village accomplish a great deal, even if some groups still bear more risk than others.
Extending the model to locations and dates 39:30
The setup generalizes to many locations and many dates, so the commodity space has a dimension equal to the number of locations times the number of dates. People still get utility from consumption, but they only hold positive endowments in the location where they happen to be at a given time. Each person can be paired with another traveler or left alone, echoing the isolated pairings from the earlier Ostroy-Starr framework. There is one good per date and location, and there is no transportation, production, or storage of goods, though financial claims can be carried from place to place.
Notation for securities across places and dates 41:31
Consumption and endowments are indexed by person, location, and date, and securities are added on top of that: a security represents units of consumption promised by one person, issued at one date, and coming due at a later date. Prices for these securities can include even more indexes, since a security can be priced at a different location and date than where it was issued. A security only has a meaningful price when there is an unbroken chain connecting the original issuer to whoever currently holds it, whether that connection runs directly or through a sequence of other traders.
Rules governing debt and budgets 44:03
Issuers must eventually demand back everything they issued, which is called the no-redemption rule, and traders must acquire a security before they can sell it, meaning demand can never be negative once past history is summed up. Each person's budget constraint says that any surplus of endowment over consumption at a given place and time gets used to buy securities, while any deficit must be covered by selling securities acquired earlier. A debt equilibrium is then defined as a set of consumption and debt choices, together with prices, that maximize utility subject to these trading rules while clearing markets, meaning total excess consumption demand sums to zero and security demand equals security supply everywhere.
Matching debt equilibrium to complete markets 47:00
The goal is to show that trading these securities can reproduce the outcome of an idealized complete-markets equilibrium, where all location- and date-specific goods are priced and traded once at an initial date. In that complete-markets version, prices are quoted in a unit of account, and each household's valued excess demands sum to zero, just as in a standard competitive equilibrium. The guess for how to price debt is that the ratio of complete-markets prices at the redemption date and the issue date tells you the right debt price, since redemption is always one-to-one in the promised good.
Solving with five key equations 52:32
Although the full system has many people, dates, and locations, it turns out you do not need to solve every budget constraint separately. By judiciously combining five of the sequential budget constraints, plus market-clearing conditions, the problem reduces to just five unknowns rather than the full set of thirty-two excess demands. After some matrix manipulation, four of the resulting equations pin down the non-circulating debts needed to reach the target allocation, and a fifth equation determines whether a given quantity of circulating debt, issued by a particular person at a particular location, can complete the job.
The coordination problem and what happens when it fails 56:04
There are infinitely many ways to arrange the debt issues that achieve the same underlying allocation, but agents born into a particular location cannot automatically know what is happening elsewhere. If two locations each mistakenly believe they are the sole issuer of the circulating security, the model shows that people carrying that security discover its price has collapsed once they arrive at another location. There is enough information for everyone to see the mistake by date two, but adjustments in borrowing and lending come too late to fully fix things, so the crisis unfolds slowly even though prices move abruptly. In a worked example with log utility, some people who end up holding the mispriced circulating debt suffer real utility losses, while others unexpectedly benefit, showing how uneven the damage can be.
Historical echoes and the case for coordinated issuance 1:04:04
The lesson is not that private or circulating securities should be banned, but that their issuance needs to be coordinated when participants understand enough about the underlying economy, a point the literature on tokenization and digital assets has not yet raised. This connects to Bagehot's account of the London money market, where small businesses discounted IOUs through bill brokers, and where the resulting circulating bills could still trigger a crisis without coordination. That history maps onto the long-running debate between the real bills doctrine and the quantity theory of money, over whether restricting the money supply or allowing financial intermediation is the right way to keep prices stable, a debate connected to a paper by Wallace and Sargent. The same coordination issue shows up in low- and middle-income countries dealing with parallel electronic accounts and currency, and in the fragmentation problems said to be hurting decentralized finance today.
Smart contracts on Ethereum, briefly reviewed 1:08:00
A blockchain is a distributed ledger that records transactions in blocks, with a consensus algorithm agreeing on which blocks are valid, and Bitcoin's transactions simply move cryptocurrency between addresses. Ethereum generalizes this by giving the blockchain a complete programming language, allowing arbitrary functionality beyond simple balance transfers, an idea people were already reaching for soon after Bitcoin appeared. Ethereum introduces two account types: ordinary accounts for balances and transfers, and contract accounts that store code and data, receive messages, update their own state, and send out further transactions as a result. This generalizes the notion of state beyond simple currency balances so that it can also represent the logic and data of a running contract.
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