Question

Omega Custom Cabinets produces and sells custom bathroom vanities. Assume that labor is the only input that varies for the firm. The firm has determined that if it hires 10 workers, it can produce and sell 20 vanities per week. If it hires 11 workers, it can produce and sell 22 vanities per week. It sells each vanity for $800, and it pays each of its workers $1,000 per week. Which of the following is correct?
a. For the 11th worker, the marginal profit is $600.
b. For the 11th worker, the marginal revenue product is $2,000.
c. The firm is maximizing its profit.
d. If the firm is employing 11 workers, then its profit would increase if it cut back to 10 workers.

Answer 1

Answer:

The answer is option a). For the 11th worker, the marginal profit is $600.

Explanation:

Step 1: Determine the initial profit for the 10 workers as shown;

initial profit=revenue from sales-cost of labor

where;

revenue from sales=sale per unit×number of units

revenue from sales=800×20=$16,000

cost of labor=cost per unit×number of workers

cost of labor=1,000×10=$10,000

replacing;

initial profit=16,000-10,000=$6,000

Step 2: Determine the final profit for the 10 workers as shown;

final profit=revenue from sales-cost of labor

where;

revenue from sales=sale per unit×number of units

revenue from sales=800×22=$17,600

cost of labor=cost per unit×number of workers

cost of labor=1,000×11=$11,000

replacing;

final profit=17,600-11,000=$6,600

Step 3: Determine the marginal profit as shown;

marginal profit=final profit-initial profit

where;

final profit=$6,600

initial profit=$6,000

replacing;

marginal profit=6,600-6,000=$600

The marginal profit for the 11th worker=$600