7.2 Modeling Tool #2: Comparative Statics

In Part I of the book, we introduced our first modeling tool: constrained optimization. In particular, we analyzed how Chuck maximized his utility subject to a given constraint (his PPF).

Parts II and III of this book are primarily concerned with a second modeling tool: comparative statics. This is the study of how an economic outcome, like the solution to a constrained optimization problem, changes when the underlying parameters generating that outcome change.

For example, with Chuck on his desert island, we might have asked how his optimal choice would have changed if he had gotten better at fishing, or if he had decided to devote more time to producing fish and coconuts, or if his preferences over fish and coconuts had changed.

In these two parts, we are going to establish parameterized problems for consumers and firms. In particular, we’re going to say that the constrained optimization problem consumers and firms are solving will depend on market prices. Market prices will determine the size of the consumer’s feasible set, and the slope of their constraint. Prices of resources will determine the cost structure of firms, and prices of goods will determine their revenues. In other words, our fundamental goal in the next two parts is to characterize the demand decision of consumers and the supply decision of firms as functions of prices. The end result will be perhaps the most famous encapsulation of comparative statics in economics: demand and supply curves.

To start out, let’s see how prices, together with income, determine a consumer’s feasible set.