Final.pdf - Technology Firms turn inputs into outputs...

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Technology Firms turn inputs into outputs Inputs called factors of production o Labor o Land o Raw materials o Capital – factors produced from other factors § Buildings § Tractors § Computers Production function o Represents technological constraints o Y = f(x 1 ,x 2 ) o Y is the maximum amount of output from x 1 units of factor one and x 2 units of factor two o Production function is an isoquant curve o Iso means equal, quant means quantity o Isoquant is a curve that shows all the combinations of inputs that yield the same level of output § Ex.) set output to 100 § X-axis: workers per day § Y-axis: units of capital per day o Find the cheapest way to produce a fixed amount of output Fixed proportions (perfect complements) o Ex.) One person and one shovel Perfect substitutes o Ex.) Humans or robots Cobb-Douglas o Ex.) Workers and office space Marginal product o Analogous to marginal utility o MP 1 (x 1 ,x 2 ) § Given current use of x 1 units of factor 1 and x 2 units of factor 2, how much extra output could be achieved with one more unit of factor 1 o MP 2 (x 1 ,x 2 ) § Given current use of x 1 units of factor 1 and x 2 units of factor 2, how much extra output could be achieved with one more unit of factor 2 Technical rate of substitution (TRS) o Equivalent term is marginal rate of technical substitution (MRTS) similar to MRS o How much extra units of factor 2 do we need to keep output constant if giving up a small amount of factor 1 o MRTS is the slope of the isoquant, analogous to MRS o TRS (x 1 ,x 2 ) = -MP 1 (x 1 ,x 2 ) / MP 2 (x 1 ,x 2 ) Diminishing marginal product o Adding more of one factor, holding the other factor constant , the marginal increase in output diminishes o Second derivative of factor one and two is less than 0 o Cobb-Douglas § If the exponent of the factor is less than one, then there will be a diminishing marginal product § Second derivative will for sure be negative
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Diminishing technical rate of substitution o When you increase factor 1 and decrease factor 2 along isoquant, the absolute value of the TRS falls o Implied through the convexity of isoquants (analogous to diminishing MRS) Diminishing technical rate of substitution (DTRS) does not require diminishing marginal product o Consider Cobb-Douglas example: F(x 1 ,x 2 ) = Ax 1 a x 2 b o Diminishing TRS for all values of a and b o But, only diminishing marginal product (second derivatives are negative) when the exponents of the function are less than 1 How does output respond to increases in all factors o Proportional increase: multiply all factors by t >1 o
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