4. TP L = - L 3 + 8 L 2 + 187 L MP L = - 3 L 2 + 16 L +187 How many units of lab

Question

4. TPL= - L3+ 8 L2+ 187 L

     MPL= - 3 L2+ 16 L +187

How many units of labor (L*) or the number of laborers should the firm hire to maximize output (TPL)

What is the total amount of output (TPL) produced

What is the average product of labor (APL)

   5. TPL= - 0.025 L3 + 5 L2+ 1000 L

        MPL= - 0.075 L2+ 10 L +1000

How many units of labor (L*) or the number of laborers should the firm hire to maximize output (TPL)

What is the total amount of output (TPL) produced

What is the average product of labor (APL)

-2-

       6. TPL= - 0.4 L3 + 4 L2+ 40 L

            MPL= - 1.2 L2+ 8 L +40

How many units of labor (L*) or the number of laborers should the firm hire to maximize output (TPL)

What is the total amount of output (TPL) produced

What is the average product of labor (APL)

please show work

Explanation / Answer

The firm should hire till MPL equals zero.

4. MPL= - 3 L2+ 16 L +187

3L2-16L-187 = 0

On solving quadtratic eqution we get L=11

The firm shoudl hire 11 labors, the total output will be:

TPL= - L3 + 8 L2+ 187 L

TPL = 1694

The total output is 1694. Average product is total product divided by labor input units

1694/11 = 154

APL = 154

5. MPL= - 0.075 L2+ 10 L +1000

L = 200

TPL = - 0.4 L3 + 4 L2+ 40 L

TPL = 136000

APL = Q/L

APL = 136000/200 = 680

6. MPL= - 1.2 L2+ 8 L +40

Equating MPL to zero we get

0= - 1.2 L2+ 8 L +40

L = 10

TPL= - 0.4 L3 + 4 L2+ 40 L

TPL = 400

APL =TPL / L

APL = 400/10 = 40

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.