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# ch09 - Chapter 9 Production Functions Production Function...

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Unformatted text preview: Chapter 9 Production Functions 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 capital ( k ) and labor ( l ) q = f ( k , l ) Marginal Physical Product • Marginal physical product is the additional output that can be produced by employing one more unit of that input – holding other inputs constant (we use partial derivatives) 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 • The marginal physical product of an input depends on how much of that input is used • In general, we assume diminishing marginal productivity 11 2 2 < = = ∂ ∂ = ∂ ∂ f f k f k MP kk k 22 2 2 < = = ∂ ∂ = ∂ ∂ f f f MP ll l l l • Changes in the marginal productivity of labor over time also depend on changes in other inputs such as capital – we need to consider f l k which is often > 0 Average Physical Product • Labor productivity is often measured by average productivity l l l l ) , ( input labor output k f q AP = = = • Note that AP l also depends on the amount of capital employed A Two-Input Production Function • Suppose the production function for flyswatters is q = f ( k , l ) = 600 k l- k l • To construct MP l and AP l , we must assume a value for k let k = 10 • The production function becomes A Two-Input Production Function • This implies that q has a maximum value: 120000 l- 3000 l = 0 ⇒ 40 l = l ⇒ l = 40 • Labor input beyond l = 40 reduces output • To find average productivity, we hold k =10 and solve AP = q / l = 60000 l- 1000 l Isoquant Maps • To illustrate the possible substitution of one input for another, we use an isoquant map • An isoquant shows those combinations of k and l that can produce a given level of output ( q ) Isoquant Map l per period k per period • Each isoquant represents a different level of output – output rises as we move northeast q = 30 q = 20 Marginal Rate of Technical Substitution ( RTS ) l per period k per period q = 20- slope = marginal rate of technical substitution ( RTS ) • The slope of an isoquant shows the rate at which l can be substituted for k l A k A k B l B A B RTS > 0 and is diminishing for increasing inputs of labor Marginal Rate of Technical Substitution ( RTS ) • The marginal rate of technical substitution ( RTS ) shows the rate at which labor can be substituted for capital – holding output constant along an isoquant ) for ( q q d dk k RTS =- = l l RTS...
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ch09 - Chapter 9 Production Functions Production Function...

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