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Chapter 17 / The Circular Flow and General Equilibrium

# 17.1 The Circular Flow

In Part I of this book, we examined the problem of Chuck, stranded on a desert island. He was the only producer and consumer, and there was no money: his economic problem was to maximize his utility given the resource constraints and technology available to him.

In the subsequent chapters, we’ve examined the behavior of consumers and firms operating in a marketplace.

• Consumers had an exogenously given income $m$ and faced exogenously given prices $p_1$ and $p_2$. The solutions to a consumer’s problem were the demand functions $x_1^\star(p_1,p_2,m)$ and $x_2^\star(p_1,p_2,m)$. We didn’t specify where the consumer’s income came from.
• Firms bought labor and sold their output at exogenously given prices $w$ and $p$. The solutions to a firm’s problem were the supply function $q^\star(w,p)$ and the labor demand function $L^\star(w,p)$. We didn’t specify what happened to the wages the firm paid, nor where its profit went.

To conclude our analysis of this model, we are going to “close” it by assuming that all the money received by firms becomes consumers’ income. Put another way, we’ll “close the circle” on the famous “circular flow” diagram you probably saw in Econ 1, in which consumers sell their resources (i.e. their labor, capital, and entrepreneurial ability) in resources markets, and buy goods in product markets; and firms buy those same resources to produce and sell those same goods. In this closed system, the amount of money received by firms must equal the amount that is returned to consumers. That is, if a firm uses labor ($L$) to produce output ($q$), we have previously written firms’ profit functions as $$\pi = pq - wL$$ We can rewrite this identity as $$pq = \pi + wL$$ That is, a firm’s revenue (the price times its quantity of output) goes into two places: as profits to its owners, and to the wages it pays its workers. All of that money goes to people (worker/consumer/firm owners) as their income. In other words, if an economy produces some amounts $Y_1$ and $Y_2$ of goods 1 and 2, then the total income to consumers must be $$M = p_1Y_1 + p_2Y_2$$ When we’re done with this chapter, we’ll have solved for the equilibrium quantities of all goods (and the resources used to produce them) solely as a function of the resources available, the production functions, and the utility functions. And what we’ll find — which is probably no surprise — is that the outcome of this competitive general equilibrium is exactly the same outcome as a “social planner” would choose to maximize utility subject to the PPF.

One giant assumption to note before we get started: we’ll be modeling consumers in the market “as if” they’re a single agent with a utility function that can be used to find the optimal point along the PPF. This is patently false: there are millions of people with different preferences, and there’s no easy way to aggregate those preferences into a single utility function. There are definitely more refined versions of this model, and if you choose to proceed further in your studies, you’ll study them. But for now, we’ll keep it simple and assume that the preferences of a whole society can be modeled “as if” they had one utility function with well-behaved indifference curves.

Copyright (c) Christopher Makler / econgraphs.org