## Related questions with answers

Economists use production functions to describe how the output of a system varies with respect to another variable such as labor or capital. For example, the production function $P(L)=200 L+10 L^2-L^3$ gives the output of a system as a function of the number of laborers $L$. The average product $A(L)$ is the average output per laborer when $L$ laborers are working; that is $A(L)=P(L) / L$. The marginal product $M(L)$ is the approximate change in output when one additional laborer is added to $L$. laborers; that is, $M(L)=\frac{d P}{d L}$. (a). For the production function given here, compute and graph $P, A$, and $M$. (b). Suppose the peak of the average product curve occurs at $L=L_0$, so that $A^{\prime}\left(L_0\right)=0$. Show that for a general production function, $M\left(L_0\right)=A\left(L_0\right)$

Solution

Verified$(a)$ Plotted using Desmos Graphing Calculator.

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Vector Mechanics for Engineers: Statics

8th Edition•ISBN: 9780072976878Elloit R Eisenberg, E. Russell Johnston, Ferdinand Beer#### Thomas' Calculus

12th Edition•ISBN: 9780321757616George B Thomas Jr, Joel D. Hass, Maurice D. Weir#### Calculus for Scientists and Engineers

1st Edition•ISBN: 9780321785442Bernard Gillett, Eric Schulz, Lyle Cochran, William L. Briggs#### Single Variable Calculus for Scientists and Engineers: Early Transcendentals

1st Edition•ISBN: 9780321785503Bernard Gillett, Lyle Cochran, William L. Briggs## More related questions

1/4

1/7