# Economics Output Maximization and Profit Maximization

What you are solving for in these problems is the optimal input combination based either on what I call Solution #1 and Solution #2; Solution #1 guarantees output maximization and Solution #2 guarantees profit maximization. Use them where appropriate. Use the optimization procedure to get answers not an Excel result.

1. The owner of the Hughes Car Wash believes that the relationship between the number of cars washed and the labor input is:

Q= -.8 + 4.5L - .3L2 where Q is the number of cars washed per hour and L is the number of people hours employed per hour.

The firm receives $5 for each car washed and the hourly wage rate for each person employed is $4.50. The cost of other inputs such as water is trivial and hence they are ignored.

a) How many people should be employed to maximize profit?

b) What will be the firm's hourly profit?

2. Find the optimal input combination for the following:

Q= 30X + 2XY -.5X2 -.5Y2 where Q is total output, X is worker hours, and Y is machine tool hours

Given that the price of X is $25.00 per unit of X and the price of Y is $40.00 per unit of Y and MR is $.50, find the optimal input combination for this production relationship.

3. In the Elwyn Company, the relationship between output (Q) and the number of hours of skilled labor (S) and unskilled labor (U) is as follows:

Q= 300S + 200U -.2S2 -.3U2

The hourly wage of skilled labor is $10.00 per unit and the hourly wage of unskilled labor is $5.00 per unit. The firm can hire as much labor as it wants at these wage rates.

A) Elwyn's chief engineer recommends that the firm hire 400 hours of skilled labor and 100 hours of unskilled labor. Evaluate this recommendation.

B) If the Elwyn Company decided to spend a total of $5,000 on skilled and unskilled labor, how many hours of each type of labor should it hire?

C) If the price of a unit of output is $10.00, how many hours of unskilled and how many hours of skilled labor should the company hire?

See attached file for full problem description.

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#### Solution Summary

Economics Output Maximization and Profit Maximization are explored.

Managerial Economics - Clarification

13. Suppose that the firm's Production Data is given in the following schedule (where Q is the level of output).

Workers Output

Q (units)

0 0

1 600

2 1000

3 1290

4 1480

5 1600

6 1680

If P=$50 and w=$14,500, how many workers should the firm hire to maximize profits?

Workers Output (Q) MPL

0 0 ---

1 600 600

2 1000 400

3 1290 290

4 1480 190

5 1600 120

6 1680 80

What is 2 = $14500? w=$14,500.

9. Suppose that the firm's cost function is given in the following schedule (where Q is the level of output).

Output

Q (units) Total Cost

0 7

1 25

2 37

3 45

4 50

5 53

6 58

7 66

8 78

9 96

10 124

Determine the:

(a) Marginal cost schedule

See table below.

(b) Total cost schedule

Output (Q) Total Cost MC

0 7 ---

1 25 18

2 37 12

3 45 8

4 50 5

5 53 3

6 58 5

7 66 8

8 78 12

9 96 18

10 124 28

E = 1.58689459

What problem did this address?

Workers Output (Q) MPL

0 0 ---

1 600 600

2 1000 400

3 1290 290

4 1480 190

5 1600 120

6 1680 80