Ch 7 - Production Theory

# Ch 7 - Production Theory - CHAPTER 7 PRODUCTION THEORY...

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CHAPTER 7: PRODUCTION THEORY Production Theory: - managers must decide: - what to produce for the market - how to produce it in the most efficient/ least cost manner - Basic Production Theory: An application of the constrained optimization = the firm attempts either to minimize the cost of producing a given level of output or to maximize the output attainable with a given level of cost Production: Production Function: is a table, graph or an equation showing the highest output that a firm can produce from every specified combination of inputs given the state of technology Average & Marginal Product of an Input: - Average Prod of an Input: Total Product Total Units of Input - Marginal Product: ∆Total Product ∆ Units of Input = the addition to Total Output resulting from the addition of the last unit of the input holding constant the amount of other inputs Relationship: - MProd > AProd AProd Increasing - MProd < AProd AProd Decreasing - MProd = AProd AProd @ Max Calculation: - MProd = ∆Q/∆x - AProd = Q/x = ∆(Q/x)/ dx = [x(∆Q/∆x) – Q(∆x/∆x]/x 2 1/x[(∆Q/∆x) – (Q/x)] (recall ch 2) - AProd max when ∆(Q/x)/ ∆x = 0, then ∆(Q/x)/ ∆x = 1/x[(∆Q/∆x) – (Q/x)] = 0 This means that ∆Q/∆x MUST = Q/x, when AProd is a maximum when AProd (Q/x) is a maximum MProd (∆Q/∆x) = ApProd Total, Average & Marginal Product: - Marginal Prod = slope of Total Prod - Max/Min Function 1 st derivative & set = 0 - @ pt A Total Prod = highest = MProd highest - @ pt C Total Prod = max MProd/ Slope = 0 MProd intersects horizontal axis 30 90 130 161 184 196 Total Product Q from hiring fourth worker Q from hiring third worker Q from hiring second worker Q from hiring first worker L { ± ‚“ @ L { ± ‚“ @ L { ± ‚“ @ L { ± ‚“ @ ² ² diminishing marginal returns Units of Number of 6 2 3 4 5 1

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Ch 7 - Production Theory - CHAPTER 7 PRODUCTION THEORY...

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