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ajaz_eco_204_2012_2013_chapter_14_PMP_Algebra

ajaz_eco_204_2012_2013_chapter_14_PMP_Algebra - University...

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 1 ECO 204 Chapter 14: The Mathematics of the Profit Maximization Problem (this version 2012-2013) Department of Economics (STG), ECO 204, Sayed Ajaz Hussain _________________________________________________________________________________________________ C HAPTER 14: The Mathematics of the Profit Maximization Problem (for use in future chapters) 1 No practice problems for this chapter. This chapter develops a model that will be used in following chapters Updated: 3/17/2013 Fixed typos are shaded yellow 1. Introduction In the previous two chapters, we modeled a firm’s short and long run cost minimization problem (CMPs) and showed how the firm chooses the optimal mix of the cost minimizing inputs required to produce an exogenously given target output level 2 . Over the next few chapters we will see that the firm can determine this target output level by any number of criteria such as the target output being the profit maximizing output, or the revenue maximizing output, or the average cost minimizing output, etc. Since many models in the coming chapters involve profit maximization, in this chapter we set up and analyze a general profit maximization problem (PMP) which serves as a “template” which can be modified and used in a variety of settings such as the target output of a profit maximizing competitive firm, or the target output of a profit maximizing monopolist charging uniform prices, or the target output of a profit maximizing monopolist charging 1 st degree price discrimination price, etc. Before reading this chapter, you might want to review chapter 1. 2. The General PMP We assume: For simplicity we consider a firm producing a single product/service (“good”) and assume there is no strategic interaction between firms which means that we can tr eat all other firms as “dormant players” never respond ing to the firm’s actions (we will relax this assumption in game theory). We assume the firm is in the short run and has solved and its short run Cost Minimization Problem (CMP) for an arbitrary target output level and therefore knows its short run cost function . We also assume that the firm has a finite capacity and a minimum production constraint . Under these assumptions, the firm’s Profit Maximization Problem (PMP) is: 1 Thanks: Asad Priyo, Adam Michael Lavecchi, and especially Akber Nafeh for typing practice problems and solutions. For feedback, comments and typos please e-mail [email protected] Thanks to the following for feedback: Corrado Vindigni, Arshaq Meraj.
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