ASSUME THE PRODUCTION FUNCTION GIVEN AS Q=7L+10L2-L3 THE AMOUNT OF EMPLOYMENT WHICH MAXIMIZES THE TOTAL PRODUCTION OR AT WICH MARGINAL PRODUCT IS ZERO
To find the amount of employment that maximizes total production or at which the marginal product is zero, we need to find the derivative of the production function with respect to employment and set it equal to zero.
Given the production function: Q = 7L + 10L^2 - L^3
1. Find the derivative of the production function with respect to L:
dQ/dL = 7 + 20L - 3L^2
2. Set the derivative equal to zero and solve for L:
7 + 20L - 3L^2 = 0
Now, we can solve this quadratic equation to find the critical points.
3. Rearrange the equation to standard quadratic form:
3L^2 - 20L - 7 = 0
4. Solve the quadratic equation using factoring, completing the square, or using the quadratic formula.
Alternatively, you can use an online equation solver or a graphing calculator to find the roots of the equation. The two values of L that satisfy the equation will give you the points where the marginal product is zero.
Once you find the values of L where the marginal product is zero, you can evaluate the production function at those points to find the respective quantities of total production.