ch10 - Chapter 10 Cost Functions Definitions of Costs...

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Chapter 10 Cost Functions
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Definitions of Costs Accounting and economic costs are different Accountant’s stress out-of-pocket expenses, depreciation, and other bookkeeping entries economists focus more on opportunity cost Labor Costs to accountants, labor costs are current expenses and hence costs of production to economists, labor is an explicit cost labor services are contracted at some hourly wage ( w ) and it is assumed that this is also what the labor could earn in alternative employment
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Definitions of Costs Capital Costs accountants use the historical price of the capital and apply some depreciation rule to determine current costs economists refer to the capital’s original price as a “sunk cost” and instead regard the implicit cost of the capital to be what someone else would be willing to pay for its use we will use v to denote the rental rate for capital
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Definitions of Costs Costs of Entrepreneurial Services accountants believe that the owner of a firm is entitled to all profits revenues or losses left over after paying all input costs economists consider the opportunity costs of time and funds that owners devote to the operation of their firms part of accounting profits would be considered as entrepreneurial costs by economists
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Economic Cost The economic cost of any input is the payment required to keep that input in its present employment the remuneration the input would receive in its best alternative employment
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Two Simplifying Assumptions There are only two inputs homogeneous labor ( l ): labor-hours homogeneous capital ( k ): machine-hours entrepreneurial costs are included in capital costs Inputs are hired in perfectly competitive markets firms are price takers in input markets
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Economic Profits Total costs for the firm are given by total costs = C = w l + vk Total revenue for the firm is given by total revenue = pq = pf ( k , l ) Economic profits ( π ) are equal to π = total revenue - total cost π = pq - w l - vk π = pf ( k , l ) - w l - vk
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Economic Profits Economic profits are a function of the amount of capital and labor employed we could examine how a firm would choose k and l to maximize profit “derived demand” theory of labor and capital inputs for now, we assume that the firm has already chosen output level ( q 0 ) and wants to minimize its costs
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Cost-Minimizing Input Choices • To minimize the cost of producing a given q 0 , a firm should choose a point on the isoquant at which the RTS is equal to the ratio w / v it equates the rate at which k can be traded for l in the production process to the rate at which they can be traded in the marketplace • Minimize total costs given q = f ( k , l ) = q 0 Lagrangian: L = w l + vk + λ [ q - f ( k , l )]
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Cost-Minimizing Input Choices Dividing the first two conditions we get ) for ( / / k RTS k f f v w l l = = The cost-minimizing firm should equate the
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ch10 - Chapter 10 Cost Functions Definitions of Costs...

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