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# L12prodfcns_myversion - Lecture 12 Production Functions Key...

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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
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: k k f k q MP capital of product physical marginal l l l f q MP labor of product physical marginal
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 f f k f k MP kk k 0 22 2 2 f f f MP ll l l l

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Diminishing Marginal Productivity K q This graph demonstrates both (i) positive marginal product of capital and (ii) diminishing marginal productivity of capital
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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Average Physical Product Labor productivity is often measured by average productivity AP L = Output / Labor = Af(K,L) / L Note that AP L
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