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Introduction to Modern Economic Growth for the first part of the book, where our focus will be on competitive economies They will not be as relevant (at least if used in their current form), when we turn to models of technological change, where product markets will be monopolistic or when we study certain classes of models of economic development, where various market imperfections will play an important role Second, the most general class of dynamic general equilibrium models will not be tractable enough for us to derive sharp results about the process of economic growth For this reason, we we will often adopt a range of simplifying assumptions The most important of those is the representative household assumption, which enables us to model the demand side of the economy as if it were generated by the optimizing behavior of a single household We saw how this assumption is generally not satisfied, but also how a certain class of preferences, the Gorman preferences, enable us to model economies as if they admit a representative household We also discussed how typical general equilibrium economies can be modeled as if they admit a representative firm In addition, in this chapter we introduced the first formulation of the optimal growth problems in discrete and in continuous time, which will be useful as examples in the next two chapters where we discuss the tools necessary for the study of dynamic optimization problems 5.11 References and Literature This chapter covered a lot of ground and in most cases, many details were omitted for brevity Most readers will be familiar with much of the material in this chapter Mas-Colell, Winston and Green (1995) have an excellent discussion of issues of aggregation and what types of models admit representative households They also have a version of the Debreu-Mantel-Sonnenschein theorem, with a sketch proof The representative firm theorem, Theorem 5.4, presented here is rather straightforward, but I am not aware of any other discussion of this theorem in the literature It is important to distinguish the subject matter of this theorem from the Cambridge controversy in early growth theory, which revolved around the issue of whether different types of capital goods could be aggregated into a single capital index (see, 248