L12prodfcns-1

L12prodfcns-1 - Lecture 12: Production Functions Key Terms...

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Lecture 12: Production Functions
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Key Terms in Lecture • Production function • Technology • Inputs • Marginal (physical) product –Diminishing marginal product • Average (physical) product • Isoquant • Marginal rate of technical substitution
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Production Function • The firm’s production function for a particular good ( q ) shows the maximum amount of the good that can be produced – using alternative combinations of inputs – and for a given level of technology • Suppose the level of technology is A and there are n inputs: i 1 , i 2 , …, i n – Then q = A*f(i 1 ,i 2 ,…,i n ) • Suppose the inputs are capital ( k ) and labor ( l ) – Then q = A*f(k,l) • The production function determines how much a firm produces as a function of its inputs.
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Marginal Physical Product • Marginal physical product (often just the marginal product ) is the additional output that can be produced by employing one more unit of that input holding other inputs constant –Assuming a positive marginal physical product for every input seems natural (and we will often, but not always make this assumption) –Suppose A = 1. Then: ! ! " ! # $% ! " " ! ! capital of product physical marginal l l l " # $% ! " " ! ! labor of product physical marginal
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Diminishing Marginal Productivity • Marginal physical product depends on how much of that input is used • In general, we assume diminishing marginal productivity – If you add a unit of capital, it increases output, but at a decreasing rate • With one machine and one worker, an additional machine may increase output by a bunch • But with a million machines and one worker, an additional machine probably hardly increases output • Again, suppose A = 1. Then: 0 11 2 2 # ! ! " " ! " " " " ! " ! $% !! ! 0 22 2 2 # ! ! " " ! " " " " " $% ll l l l
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Diminishing Marginal Productivity # • This graph demonstrates both (i) positive marginal product of capital and (ii) diminishing marginal productivity of capital
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Diminishing Marginal Productivity • Diminishing marginal productivity led 19th century economist Thomas Malthus to worry about the effect of population growth on labor productivity – As pop rises, MP L falls (holding K and A fixed) – A hugely oversimplified version of his view: In times of plenty, people had lots of kids, this reduced the productivity of labor, society could not feed everyone, people died, and we returned to a normal state of affairs until, for whatever reason, a time of plenty occurred again, and the whole cycle repeated… (big-time simplification, so don’t quote me!) • However, MP L is much higher today than in the 19 th century… • Changes in the marginal productivity of labor also depend on changes in other inputs such as capital and on changes in technology • Malthus’ story can work if only two inputs are Labor and Land and no technological change…
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L12prodfcns-1 - Lecture 12: Production Functions Key Terms...

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