Properties of a Competitive General Equilibrium

Not surprisingly, analyzing a general-equilibrium system is more complicated than using partial equilibrium analysis, which deals with only a single market. A general-equilibrium system represents a whole economy, rather than just part of one. It may contain many different kinds of labor, machines, and land, all of which are serving as inputs to produce dozens of different kinds of computers, hundreds of different specifications of automobiles, thousands of different items of clothing, and so on. It contains services like cellular connections, college courses, and vacations to Disneyland, as well as goods like heavy construction equipment, pizzas, and cellular telephones.

The Basic Principles. What assumptions do we make in analyzing a competitive economy? We assume that all markets are perfectly competitive, i. e., they are subject to the relentless competition of many buyers and sellers. Each price, whether for an input or an output, moves flexibly enough to equilibrate supply and demand at all times. Firms maximize profits, while consumers choose their most preferred market baskets of goods. Each good is produced under conditions of constant or decreasing returns to scale. No pollution, externalities, entry-limiting regulations, or monopolistic labor unions mar the competitive landscape. Consumers and producers are well informed about prices and economic opportunities. These conditions are obviously an idealized situation. But were such an economy to exist, it would be one in which Adam Smith’s invisible hand could rule without any impediment from externalities or imperfect competition.
For this economy, we can describe consumer behavior and producer behavior and then show how they dovetail to produce an overall equilibrium. First, consumers will allocate their incomes across different goods in order to maximize their satisfactions. They choose goods such that the marginal utilities per dollar of expenditure are equal for the last unit of each commodity.

What are the conditions for the profit maximization of producers? In product markets, each firm will set its output level so that the marginal cost of production equals the price of the good. Since this is the case for every good and every firm, it follows that the competitive market price of each good reflects society’s marginal cost of that good.

Putting together these two statements yields the conditions for a competitive equilibrium. For each consumer, the marginal utility of consumption for each good is proportional to that good’s marginal cost. Hence, the marginal utility per last dollar spent on each good is equalized for every good.

An example will clarify this result. Say that we have two individuals, Ms. Smith and Mr. Ricardo, and two kinds of goods, pizza and clothing. Set the utility scale so that 1 unit equals $1.l In the consumer equilibrium, Ms. Smith buys pizza and clothing until her MU per dollar of each good is 1 (Smith) util.
Similarly, Mr. Ricardo distributes his income so that he gets 1 (Ricardo) util per dollar of spending. The pizza and clothing producers set their output levels such that price equals marginal cost, so a dollar-bundle of pizza will have a marginal cost of production of $1 for each producer, as will a dollar-bundle of clothing. If society were to produce one more dollar-bundle of pizza, the cost to society would be exactly 1 dollar’s worth of a bundle of scarce labor, land, and capital resources.

Putting these conditions together, we see that each extra dollar of consumption, by either Smith or Ricardo, yields exactly 1 extra until of subjective satisfaction, whether that extra spending is on clothing or on food. Similarly, each extra unit of spending will have a marginal or additional cost to society of 1 extra dollar of resources, and this is so whether that extra dollar is spent by Smith or Ricardo or on food or clothing.

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