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# ch07 - Chapter 9 PRODUCTION FUNCTIONS 1 Production Function...

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1 Chapter 9 PRODUCTION FUNCTIONS

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2 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. q = f ( x 1 , … , x n )
3 Production Function • We will consider production functions that depend on capital ( k ) and labor ( l ): q = f ( k , l )

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4 Marginal Physical Product • The marginal physical product , is the additional output that can be produced by increasing by a small amount one of the inputs while holding other inputs constant: k k f k f k q MP capital of product physical marginal l l f l f l q MP labor of product physical marginal
5 Diminishing Marginal Productivity • The marginal physical product of an input depends on how much of that input is used. • In general, the marginal product decreases , 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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6 Average Physical Product • Labor productivity is can also be measured by average productivity l l l l ) , ( input labor output k f q AP • Note that MP l and AP l depend on the amount of capital employed. MP k and AP k depend on the amount of labor employed.
7 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 0 ) f ( k , l ) = q 0

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8 Isoquant Map l per period k per period • Each isoquant represents a different level of output – output rises as we move outward. q = 30 q = 20
9 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

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10 Marginal Rate of Technical Substitution ( RTS
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ch07 - Chapter 9 PRODUCTION FUNCTIONS 1 Production Function...

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