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We analyze the Nash eqilibria of a one-stage game in which the nature of the strategic variables (prices or quantities) is determined endogenously. Duopolists producing differentiated products simultaneously choose either a quantity to produce or a price to charge. In the absence of exogenous uncertainty, there exist four types of equilibria with differing levels of output: (price, price), (quantity, quantity), (price, quantity), and (quantity, price). The multiplicity of equilibria stems from each firm's indifference between setting price and quantity, given its conjecture about its rival's strategy. But exogenous uncertainty about market demands, which makes firms uncertain about their residual demands, even in equilibrium, gives firms strict preferences between setting price and quantity. As a result, the number of equilibria is reduced. When uncertainty is exogenous, we analyze the effect of the slope of marginal costs, the nature of the demand disturbance, and the curvature of demand on firms' propensities to complete with price or quantity as the strategic variable. These three factors are likely to influence the nature and intensity of oligopolistic competition.

In this chapter, we deconstruct the computable general equilibrium model and describe its core elements. These include sets, endogenous and exogenous variables, exogenous parameters, behavioral and identity equations, and model closure. We describe prices, price normalization, price transmission, and the numeraire. We explain how the CGE model runs and how to carry out an experiment. A computable general equilibrium (CGE) model is a system of mathematical equations that describes an economy as a whole and the interactions among its parts. A model this comprehensive is more complex than the bicycle industry model we built in Chapter 1, but it need not be a “black box.” In this chapter, our objective is to introduce, at a general level, the model's elements and mechanics. Even so, for many students, it may suffice to skim this chapter and return to it as needed as your modeling skills progress. For now, we also set aside any consideration of the economic theory that governs behavior in the model. Here, we do not consider how the model describes the motivations behind producers’ decisions about how much to produce or consumers’ decisions about how much to buy, or a nation's choice between consumption of its domestic production and imported goods. Of course, the economic properties of a CGE model are its real heart and soul, but they also present a much broader area of study; most of the other chapters in this book address this study. In this chapter, we deconstruct the CGE model to describe its core elements. We show that a CGE model and the simple bicycle model share many features, such as exogenous and endogenous variables, market-clearing constraints, and identity and behavioral equations. We explain and compare linearized and nonlinear expressions of the behavioural equations in a CGE model. We describe how the price of a single good changes as it moves along the supply chain from producers to consumers and the implications for price transmission. We explain the practice of normalizing prices and the role of the price numeraire. We introduce model closure, which is the decision about which variables are exogenous and which are endogenous. We also describe how the CGE model runs by explaining the sequence of model calibration or consistency check, baseline model solution, and model experiment.

In Chapter 1, we assumed without justification the existence of demand functions. We provide a basis for that assumption in this chapter by considering individual preferences. In so doing, we seek not only to describe rather more completely the properties of demands but also to establish a framework within which we shall operate for the rest of the book. Section 2.1 discusses the axioms of choice and how they lead to utility functions and to the system of choice described by utility maximization. Section 2.2 is concerned with the transition from utility to the demand functions; the traditional constrained maximization approach is discussed and its drawbacks enumerated. Section 2.3 presents consumer demand in terms of cost minimization rather than utility maximization. Marshallian uncompensated demand functions, defined on prices and outlay, are contrasted with Hicksian compensated demand functions, defined on prices and utility, and the central concept of the cost function is introduced. Section 2.4 uses the apparatus of cost minimization to derive the properties of demand. Symmetry and negativity (the “law of demand”) are presented as is the Slutsky equation linking the price derivatives of compensated and uncompensated demands. The generality of these results is contrasted with those obtained through more traditional approaches. Section 2.5 is concerned with the meaning of “duality” in consumer theory, and we show how the cost function can be used as an alternative to the utility function as a representation of preferences.