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Matthias Doepke - Marcroeconomics - Chapter 5

Chapter 5 The Market-Clearing Model Most of the models that we use in this book build on two common assumptions. First, we assume that there exist markets for all goods present in the economy, and that all markets clear. Second, we assume that all agents behave competitively, which means that they take prices as given. | Chapter 5 The Market-Clearing Model Most of the models that we use in this book build on two common assumptions. First we assume that there exist markets for all goods present in the economy and that all markets clear. Second we assume that all agents behave competitively which means that they take prices as given. Models that satisfy these assumptions are called general equilibrium models. There are a number of important results that apply to all general equilibrium models regardless of what kind of goods agents or technologies are used. In this chapter we will demonstrate three of these results within a general setting. Many of the models that we use throughout the rest of the book will be special cases of the general model presented here. Since we omit most of the simplifying assumptions that we make in other chapters the treatment is more formal and mathematical than usual. Section 5.1 introduces our general equilibrium framework. In Section 5.2 we show that within this framework the general price level is undetermined. This implies that prices can be normalized without loss of generality. For example in many models we set the price of the consumption good to be one. In Section 5.3 we show that in a general equilibrium model one market clearing constraint is redundant a fact known as Walras Law. Section 5.4 presents the First Welfare Theorem which states that under certain conditions equilibria in a general equilibrium model are efficient. 5.1 A Genaral Pure-Exchgnge Oconomy We will consider an economy with many different goods and consumers. Instead of having a representative consumer we allow for the possibility that each consumer has a different utility function. However we make one simplification there is no production in the economy. The consumers have endowments of goods and can trade their endowments in 40 The Market-Clearing Model markets but there is no possibility of producing any goods in excess of the endowments.1 There are 2V different goods in the