# The invisible hand theorem

A long-run competitive equilibrium in this setting is a market quantity Q* = q* n* and a market price P such that:

• • Consumers take the price as given and equate the marginal consumption benefits u'(q*n*) = P with the price of the good;
• • Producers take the price as given and each firms chooses q to maximise its profits, so C'(q*) = P for each firm;
• • The market price P adjusts to clear the market, so that demand for the good equals supply. At market-clearing prices, consumers do not want to purchase any more units of a good, and producers do not want to supply any more units; and
• • There is free entry and exit so that the equilibrium number of firms

C(q*)

n* in the industry adjusts until profits are zero, so P = for all

firms. q*

In a long-run competitive equilibrium, since P = C(q) and since

q

marginal cost also equals price, we must have marginal cost equal to average cost. This only occurs at the minimum of the average cost curve. The long-run competitive equilibrium is shown in the diagram below. The long-run market supply curve here is assumed to be flat and is equal to the minimum of the average cost curve. The demand curve is the marginal benefit curve, u'(Q). Figure 1.2.1 Long-run competitive equilibrium

Notice that at point Q*, the marginal benefit of an additional unit of the good is equal to the marginal cost of an additional unit. Since the market demand curve reflects marginal consumption benefits, and since the slope of the long-run market supply curve reflects marginal opportunity costs, and since in a competitive equilibrium the two are equal to each other, this must be the case. But if marginal benefits equal marginal costs, this means that welfare must be maximised. Thus, a competitive equilibrium leads to an outcome that maximises welfare.

In a perfectly competitive market, consumers take prices as given and maximise their net benefits, and producers also take prices as given and maximise profits. The market price adjusts and reconciles consumer demands and producer supply. Higher prices send a signal to consumers to reduce their consumption, and for producers to bring forth more supply. Lower prices send the opposite signals. Market prices adjust until no more gains from trade are possible. This result is a version of the 'invisible hand theorem' or, more formally, the first fundamental theorem of welfare economics.