Economics Production Function MPL=Max help!

Question

 A certain production process employs two inputs--labor (L) and raw materials (R). Output (Q) is a function of these two inputs and is given by the following relationship:

          Q = 6L2 R2− .10L3 R3

Assume that raw materials (input R) are fixed at 10 units.

Determine the Number of units L that maximizes the MPL function.

Answer 1

To determine the number of units of labor (L) that maximizes the marginal product of labor (MPL), we start by understanding the given production function and deriving the MPL from it.

Given Production Function

The production function is: Q=6L²R²−0.10L³R³

Here, R (raw materials) is fixed at 10 units. We substitute R=10 into the production function to express it

solely in terms of L.

Step 1: Substitute R=10 into the Production Function

Q=6L²(10)²−0.10L³(10)³

Q=600L²−100L³

Step 2: Derive the MPL Function

The marginal product of labor (MPL) is the derivative of the production function with respect to L"

MPL=dQ/dL

MPL=d/dL(600L²−100L³)

MPL=1200L−300L2

Step 3: Maximize the MPL Function

To find the number of units of L that maximizes MPL, set the derivative of MPL (which gives the rate of change of MPL with respect to L) to zero and solve for L:

d(MPL)dL=0

d/dL(1200L−300L²)=1200−600L=0

L=2

Hope this helps.