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Chapter 7 / Utility Maximization Subject to a Budget Constraint

7.1 Decentralizing the Model


Thus far we have studied the central economic problem of scarcity and choice: in a world with limited resources, how do we choose what to do with those resources?

For Chuck on his desert island, who was simultaneously a producer and a consumer, the question boiled down to two fundamental functions:

In a modern economy, of course, you don’t produce everything you use; you’re reading this on a device that is the culmination of decades of scientific research you didn’t perform, produced using metals you neither mined nor refined, manufactured (probably) thousands of miles away by people you have never met, transported by a ship or plane or truck you didn’t build, and powered by electricity you didn’t generate from a plug in a house you didn’t construct with your bare hands. The economic forces that allow you to be reading this right now therefore involve the coordination of thousands of people, firms, and governments.

At their core, each of these economic agents is solving a constrained optimization problem, just like Chuck. However, because each agent is not consuming what they produce, we will decentralize the model into agents who produce things via a production function, and those who then consume them and enjoy their benefit. For simplicity, we’ll say that a firm buys resources (labor and capital) and sells the goods for money; and that a consumer buys those goods with money, and generates utility from their consumption. Therefore our single model of “autarky” becomes two models: one of a profit-maximizing firm, and one of a utility-maximizing consumer. In Part II of this book we will analyze the consumer’s optimization problem; in Part III we will analyze the firm’s.

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