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Lecture 1.docx

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James Bruce

Lecture 1 Inputs (factors or factors of production): things firms use to make their output Input bundle: a list of quantities, one for each input a firm can use Production function: the maximum output a firm can produce as a function of input bundles - y = output - z = input - So a production function ex: y = f(z ,z ) 1 2 Assume firms behave in such a way to maximize profits (difference between revenue and cost of production) Given that revenue depends on output, profit maximization, requires that the given level of output be produced at a minimum cost The firm’s cost minimization problem: min w z w z subject to F(z z ) > y’ where: 1 1 + 2 2 1 2 - w1 = cost per unit of input 1 - w2 = cost per unit of output 2 Opportunity cost (economic cost or cost): the opportunity cost of something is the value he value of the resources used to obtain it in their best alternative --- Ex: you tie up $1000000 of your savings in your factory for a year. The return this money could have earned elsewhere (bond) is part of the opportunity cost of the factory. - Short run: one input is fixed, the other is variable - Long run: both inputs are variable - Suppose z is fixed in SR (z ) 2 2 - Y = F(z 1z 2 = TP(z 1, TP = total product Marginal product: rate of change of output as one input increases (holding the other constant) - MP1 = dF(z ,z1)/2z 1 - MP2 = dF(z ,z1)/2z 2 - MP = dTP(z )/d1 1 - Free disposal: firms can costlessly throw away inputs. By assuming free disposal, we get that: o MP >= 0 Diminishing MP: as the quantity of an input gets large, its MP approaches zero Average Product (AP): AP = TP/z 1 Average-Marginal Relationships: - Margin > Average: Average increasing - Margin = Average: Average constant - Margin < Average: Average decreasing - dAP/dz = 1TP*z /dz 1 TP 1 - dAP/dz = 1/z (MP1AP) Cost Stuff In the short run, the cost-minimizing quantity of the variable input is found by inverting the TP - z1*=TP (y) Variable Cost (VC): cost arising from variable input - VC = w z1 1 Fixed Cost (FC): costs arising from the fixed input - FV = w z 2 2 Short-run total costs (STC) - STC = VC + FC Short-run marginal costs (SMC): rate of change of costs as output changes - SMC = dVC/dy = dSTC/dy because there is no change in fixed cost Average Variable Cost (AVC) - AVC = VC/y Short-run Average Cost (SAC) - SAC = STC/y Average Fixed Cost (AFC) - AFC = FC/y Note: SAC = AVC + AFC and that the average-marginal relationship holds for: - SMC and AVC - SMC and SAC VC = w z
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