ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 1 ECO 204 Chapter 12: a Firm’s Cost Minimization Problem (this version 2012-2013) Department of Economics (STG), ECO 204, Sayed Ajaz Hussain _________________________________________________________________________________________________ C HAPTER 12: The Long Run Cost Minimization Problem 1 Updated: 3/11/2013 Fixed typos are shaded yellow 1. Introduction In the previous chapter we modeled the firm as a “black box” entity which uses its “technology and management” to transform inputs into the output of a product/service 2 : Depending on whether the firm is in the short or the long run the firm’s output in the “production period can be modeled by a short run production function (when at least on input is fixed) or a long run production function (when no input is fixed) according to the following equations where level of management and technology at the firm: ( ) ( ) In this and the next chapter, we analyze a firm with an exogenously given (short or long run) production function, exogenously given uniform input prices, and an exogenously given strictly positive target output level that must be produced in a production period 3 . We will model this firm’s choice of the cost minimizing mix of inputs needed to produce the target output in that production period -- this model is known as the Cost Minimization Problem (CMP): 1 Thanks: Asad Priyo, Adam Michael Lavecchi, this track for much needed boosts, and especially Akber Nafeh for preparing practice problems from past HWs, tests and finals. For feedback, comments and typos please e-mail [email protected] Note to self: Develop stronger connection between returns to scale and economies of scale to show the concepts are the same when the inputs expansion path is linear and different otherwise. Thanks to following for feedback: Arshaq Meraj. 2 We will examine production of several goods/services in later chapters. 3 This exogenously given output may be a contracted output, or the revenue maximizing output, or the profit maximizing output, etc. Regardless, we take this target output level as given (a parameter). Inputs "Black Box Firm" Output of a product/service
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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 2 ECO 204 Chapter 12: a Firm’s Cost Minimization Problem (this version 2012-2013) Since the firm can be in the short or the long run, there are two versions of the CMP. In this chapter we develop the long run CMP in which the firm chooses the optimal cost minimizing mix of all inputs needed to produce the target output over the production period: ( ) In the next chapter we develop the short run CMP in which the firm (given the inputs are fixed) chooses the optimal cost minimizing mix of variable inputs needed to produce the target output over the production period: ( ) First, l et’s get an intuitive feel for the CMP by reviewing the all too familiar two good UMP for a consumer with monotone preferences: ( ) For illustrative purposes consider this Cobb-Douglas UMP: In any UMP, the constraint is the consumer’s income (“ budget ”) and the objective is to maximize utility:
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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.
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