Answer to Question #262823 in Microeconomics for JODE

Question

A firm’s short-run marginal product of labour function is 3 22 5. 2 MP   L  L  Use indefinite integrals to solve for the total product function.What increase in the total product will be brought about by employing two additional units of labour if five units are currently hired?

Answer 1

complete Question

A firm’s short-run marginal product of labor function is MP = -3L^2 + 22L - 5. Use indefinite integrals to solve for the total product function.What increase in the total product will be brought about by employing two additional units of labour if five units are currently hired?

Solution

A production function illustrates the relationship between the quantity of inputs used and the quantity of output produced. It measures the quantity of output that can be produced with a given input.

The marginal product is the addition to the total product by an additional unit of input. The marginal product is calculated as the ratio of change in total product to change in the quantity of input.

$TPTP=∫MPdL\\=∫(−3L^2+22L−5)dL\\=\frac{−3L^3}{3}+\frac{22L^2}{2}−5L\\TP=−L^3+11L^2−5L$

when the quantity of labor is 5, the total product is calculated as,

$TP=−5^3+11×5^2−5×5\\=−125+275−25\\=125$

When the quantity of labor is 7, the total product is calculated as,

$TP=−7^3+11×7^2−5×7\\=−343+539−35\\=161$

Therefore the two additional labor will increase the total product by 36 units.