We focused on the choices of a single consumer in the examples 1-3. Now we will explore the implications of interactions between many consumers with heterogeneous preferences.

The partial equilibrium approach neglects indirect effects, through which changes in the market for one good may influence the market for another good. In these models we focus on price, supply and demand for a single commodity. Using general equilibrium analysis we will explore interaction between market prices and income in the next example.

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Example 4: The purpose for this example is to demonstrate the Second Welfare Theorem - if all agents have convex preferences, then there will always be a set of prices such that each Pareto efficient allocation is a market equilibrium for an appropriate assignment of endowments.

There are two commodities, two consumers, and no production. The consumers differ by commodity endowments and preferences:

A & B - two representative consumers (each represent multiple consumers with the same endowments and preferences).

X & Y - two commodities. There are fixed endowments of both goods for each consumer.

The competitive equilibrium prices: supply=demand for both goods & both agents spend an amount equal to their endowment income.

Six parameters will be used for this model (declared as a scalars).

Assume CES utility functions for both consumers.

The key idea in this model is that trade can improve both agents' welfare. The widely used graphical framework for multi-agent exchange model is Edgeworth box.

The rate of exchange between X and Y (terms of trade) will be determined by the model.

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Please note the following important properties:

(i) so long as the transactions are voluntary, neither A nor B will be hurt by engaging in trade;

(ii) market prices are used to guide this simple economy to a Pareto efficient allocation;

(iii) there is no guarantee that the gains from trade will be fairly distributed across consumers. A competitive equilibrium may produce a significant welfare increase for one consumer while have negligible impact on the other.