Exploring Profit Maximizing Input

5. The table in the reading (reproduced below) illustrates two different ways to compute the profit-maximizing position for a firm. The profit-maximizing firm will hire four units of labor and produce 31 units of output.

Computation of the Best Input Level for the Firm
(1)
Marginal Revenue Product
(2)
Marginal Resource Cost
(3)
Labor
(4)
Output
(5)
Marginal Product
(6)
Marginal Revenue
(7)
Marginal Cost
--
--
0
0
--
--
--
$27.30
$10.00
1
13
13
$2.10
$.77
14.70
10.00
2
20
7
$2.10
1.43
12.60
10.00
3
26
6
$2.10
1.67
10.50
10.00
4
31
5
$2.10
2.00
8.40
10.00
5
35
4
$2.10
2.50

a) Suppose that there are fixed costs of $15.00 that must be paid to capital. (Recall that capital is held fixed at two units.) What will the profit of the firm be? (Hint: Compute the total revenue and total cost columns in the following table, and then subtract the latter from the former to find profit.)
b) What will happen to the profit-maximizing output if fixed costs are decreased to $10? If they are eliminated? (Hint: What will a change in fixed costs do to the marginals in the table?)
c) Suppose that the workers run the firm, and that they want to maximize profit per worker, not total profit. How much will they produce and how many workers will the firm hire, assuming that fixed costs are $15? (Hint: Compute the profit-per-worker column in the following table.)

 
Labor
Output
Total Revenue
Total Cost
Profit
Profit per Worker
0
0
$0
$15
-$15
--
1
13

2
20

3
26

4
31

5
35

(Comment: Before the fall of communism, Yugoslavia tried to implement a system of worker management. One problem that plagued them was high unemployment.)

6. Following are two tables that are similar to a table in the readings but with different numbers.

a) Complete the tables and find the profit-maximizing levels of output and labor.

(1)
Marginal Revenue Product
(2)
Marginal Resource Cost
(3)
Labor
(4)
Output
(5)
Marginal Product
(6)
Marginal Revenue
(7)
Marginal Cost
$30.00
$9.00
1
___
10
___
___
25.00
10.00
2
___
10
___
___
20.00
11.00
3
___
10
___
___
15.00
12.00
4
___
10
___
___
10.00
13.00
5
___
10
___
___

(1)
Marginal Revenue Product
(2)
Marginal Resource Cost
(3)
Labor
(4)
Output
(5)
Marginal Product
(6)
Marginal Revenue
(7)
Marginal Cost
___
3.00
.5
1
___
$4.00
___
___
3.00
1.0
2
___
3.50
___
___
3.00
1.6
3
___
3.00
___
___
3.00
2.3
4
___
2.50
___
___
3.00
3.1
5
___
2.00
___

b) Compute the supply curve of labor that exists for the first table, and the demand curve for output that exists for the second table.

Amount of Labor
Wage
*****
Amount of Output
Price
1
___
1
___
2
___
2
___
3
___
3
___
4
___
4
___
5
___
5
___

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