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Econ501aL9

# Econ501aL9 - Production Firms convert inputs such as...

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Production Firms convert inputs such as capital, labor, energy, materials, etc. into outputs of goods and services. The production function speci¯es the most output that can be produced with a given combination of inputs, based on the technology available to the ¯rm. x = f ( K; L ) Technological e±ciency occurs if the ¯rm is on its \production frontier." That is, it is impossible to achieve more output with the same inputs. The ¯rm is partially optimizing, by not wasting inputs. How- ever, technological e±ciency does not imply that the ¯rm is choosing the right bundle of inputs. (We need to factor in prices to know that.) Analogous to the more is better assumption for utility functions, we typically assume @f ( K; L ) @K > 0 and @f ( K; L ) @L > 0 :

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A production isoquant (iso meaning equal and quant meaning quantity of output) is a curve describing the set of capital-labor combinations yielding the same output, according to the production function. 0 1 2 3 4 5 K 1 2 3 4 5 L Production Isoquants Production functions and isoquants are like utility func- tions and indi®erence curves, except output can be measured and traded, while utility cannot. (Cardinal vs. ordinal)
The marginal rate of technical substitution is de¯ned to be the negative of the slope of the isoquant MRTS = ¡ dK dL j f ( K;L )=constant The MRTS is the rate at which the ¯rm would be willing to give up capital in exchange for labor.

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Econ501aL9 - Production Firms convert inputs such as...

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