Ajax Corporation is a price-taking firm in a competitive industry that employs o

Question

Ajax Corporation is a price-taking firm in a competitive industry that employs only one variable input, labor, to produce a product that sells for $2 per unit. The wage rate is $8 per unit of labor and total fixed costs are $1,000. Fill in the blanks in each column of this table as instructed by the questions below:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Units of Labor

Output

Marginal Product

Marginal Revenue Product

Average Product

Average Revenue Product

Marginal Cost

Profit

0

0

xx

xx

xx

xx

xx

______

1

400

______

______

______

______

______

______

2

950

______

______

______

______

______

______

3

1,250

______

______

______

______

______

______

4

1,350

______

______

______

______

______

______

5

1,370

______

______

______

______

______

______

6

1,373

______

______

______

______

______

______

7

1,369

______

______

______

______

______

______

8

1,364

______

______

______

______

______

______

a. Fill in the blanks in columns 3 and 5. Marginal product begins to diminish beyond ________ units of labor. Marginal product is negative beyond _________ units of labor.

b.   Compute marginal and average revenue products and fill in the blanks in columns 4 and 6. The sixth unit of labor __________________ (increases, decreases) total revenue by $__________. Decreasing labor usage from four to three units _______________ (increases, decreases) total revenue by $_________.

c.   The manager can maximize total revenue by hiring ________ units of labor. The maximum possible value of total revenue is $____________.

d.   The manager hires ________ units of labor and produces ___________ units of output in order to maximize profit. At this level of labor usage, ARP = _____________ which is ______________ (greater, less) than MRP.

e.   Compute marginal cost and fill in the blanks in column 7. At first, marginal cost ___________ (rises, falls) as marginal product rises, then marginal cost _____________ (rises, falls) as marginal product falls.

f.    The profit-maximizing level of output is ______ units because this is the last level of output for which _____________ exceeds _____________, or equivalently, _____________ exceeds _____________ .

g.   Compute profit and fill in the blanks in column 8. The optimal level of labor employment and the optimal level of output both result in an identical maximum profit level of $_____________.

h.   Now suppose total fixed cost increases to $5,000. Recalculate profit at each level of labor usage (and output) and fill in the blanks in column 9 below. When total fixed cost is $5,000, the optimal level of labor usage is _______ units of labor, and the optimal level of output is ________ units. How high must total fixed costs rise in order for it to be optimal for this firm to shut down? Explain briefly.

(1)

(2)

(9)

Units of Labor

Output

Profit

TFC = $5,000

0

0

______

1

400

______

2

950

______

3

1,250

______

4

1,350

______

5

1,370

______

6

1,373

______

7

1,369

______

8

1,364

______

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Units of Labor

Output

Marginal Product

Marginal Revenue Product

Average Product

Average Revenue Product

Marginal Cost

Profit

0

0

xx

xx

xx

xx

xx

______

1

400

______

______

______

______

______

______

2

950

______

______

______

______

______

______

3

1,250

______

______

______

______

______

______

4

1,350

______

______

______

______

______

______

5

1,370

______

______

______

______

______

______

6

1,373

______

______

______

______

______

______

7

1,369

______

______

______

______

______

______

8

1,364

______

______

______

______

______

______

Explanation / Answer

Marginal product negative beyond 6 units of labor

1) -2 -3 -4 -5 -6 -7 -8 Marginal Revenue Product Average Revenue Product Units of Labor Marginal Product Average Product Marginal Cost Total revenue Output Profit $0 0 0 xx xx xx xx xx ______ $800 1 400 400 $800 400 $800 $1,008 ($208) $1,900 2 950 550 $1,100 475 $950 $8 $884 (950*2-1008-8) $2,500 3 1,250 300 $600 416.666667 833.333333 $8 $      1,476 $2,700 4 1,350 100 $200.00 337.5 675 $8 $      1,668 $2,740 5 1,370 20 $ 40.00 274 548 $8 $      1,700 $2,746 6 1,373 3 $    6.00 228.833333 457.666667 $8 $      1,698 $2,738 7 1,369 -4 $   (8.00) 195.571429 391.142857 $8 $      1,682 $2,728 8 1,364 -5 $ (10.00) 170.5 341 $8 $      1,664 a. Marginal product start diminishing beyond 62units of labor

Marginal product negative beyond 6 units of labor

b The sixth unit of labor increases marginal revenue by $6 Decreasing labor usage from 4 to 3 unit decreases total revenue by $200 c The manager can maximize total revenue by hiring 6 units of labor Maximum revenue is$2746 d Manger hires 5 units of labor and produces 1370 units of output in order to maximize ptofit At this level ARP=$548 which is higher than MRP

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