ECON 3411 Lecture Notes - Lecture 29: Production Function, Marginal Product, Isoquant
Document Summary
Example: suppose a firm sells its output in a competitive market where its output is sold at per unit. If workers are also hired at a competitive wage of , what is the marginal productivity of the last worker: since, (cid:1839)(cid:1842)(cid:1838) = (cid:1839)(cid:1842)(cid:1838) and = , then, (cid:1839)(cid:1842)(cid:1838) = (cid:1839)(cid:1842)(cid:1838) = 40 units. The marginal productivity of the last unit of labor is 40 units. Alternatively, management should hire labor such that the last unit of labor produces 40 units. Algebraic forms of production functions constants. constants: commonly used algebraic production function forms: Linear: (cid:1843) = ((cid:1837), (cid:1838)) = (cid:1853)(cid:1837) + (cid:1854)(cid:1838), where (cid:1853) and (cid:1854) are constants. Leontief: (cid:1843) = ((cid:1837), (cid:1838)) = min{(cid:1853)(cid:1837), (cid:1854)(cid:1838)}, where (cid:1853) and (cid:1854) are. Cobb-douglas: (cid:1843) = ((cid:1837), (cid:1838)) = (cid:1837)(cid:1853)(cid:1838)(cid:1854), where (cid:1853) and (cid:1854) are: suppose that a fir(cid:373)"s esti(cid:373)ated productio(cid:374) fu(cid:374)ctio(cid:374) is: (cid:1843) = 3(cid:1837)