So far we have concentrated on one market at a time, leaving all the rest unmodeled.
Now we turn to a study of general equilibrium, in which di
erent markets interact. Our
thinking was that money could substitute for the vast array of alternative choices that
rms face. From a purely logical standpoint, it is certainly true that when
an agent chooses to buy more of the commodity under study, that will reduce her stock of
money. She will therefore be right in comparing the marginal utility of a dollar spent on
the commodity with the marginal utility of a dollar spent elsewhere. But if we describe the
elsewhere as precisely as we do the commodity itself, we might learn more about the value
of the commodity.
Changes in the demand and supply of one commodity will typically have e
the demand and supply of other commodities. If the commodities interact in the utility
functions of consumers, as when the goods are substitutes or complements, then a price
change in one commodity will obviously a
ect demand for the other. But even if the
utilities of all commodities are separable, the consumption of one commodity still might
ect the consumption of all other commodities through the agents’ budget sets.
We did not have occasion to mention the budget set so far, but clearly any potential
consumer has limited resources, and will therefore have to adjust his demand for many
goods if his income changes, or if the price of one of the goods changes. In our previous
analysis, we implicitly assumed that expenditures by each consumer would be taken out
of his stock of money, and so would not a
ect the consumption of other goods that were
already budgeted. That behavior can indeed be justi
ed by a special welfare function which
assigns constant marginal utility to one of the goods. But with almost any other utility
function, the budget set will force interactions between di
erent consumption markets.
General equilibrium is a situation in which every agent is aware of the prices of all
the goods, and buys or sells whatever he wants of every good at those prices, and the
total buying of each good just equals the total selling. In short, in general competitive
equilibrium, agents optimize and markets clear.
How does the "market" discover the equilibrium prices? More fundamentally, how can
we be sure there even are equilibriium prices that allow agents to optimize simultaneously,
while matching supply and demand? When changing a price in one market a
ects demand in
all the other markets, the simultaneous market clearing problem becomes highly nontrivial.
In the following sections we indicate that equilibrium prices do indeed exist, and we
illustrate how a central planner, who knew the preferences and endowments of every agent,
could use a computer to
nd them. Of course in reality there is no central planner who
knows everything, yet the market somehow still manages to
nd what looks like equilibrium