Suppose that a firm is currently employing 20 workers, the only variable input, at a wage rate of $60. The average product of labor is 30, the last worker added 12 units to total output, and total fixed cost is $3,600.
a. What is marginal cost?
b. What is average variable cost?
c. How much output is been produced?
d. What is average total cost?
e. Is average variable cost increasing, constant, or decreasing? What about average total cost?
f. ABC publishing uses 400 printers and 200 printing presses to produce books. A printer’s wage rate is $20, and the price of a printing press is $5,000. The last printer added 20 books to total output, while the last press added 1,000 books to total output. Is this publisher making a rational decision? Explain
What is your question??
a. What is marginal cost?
b. What is average variable cost?
c. How much output is been produced?
d. What is average total cost?
e. Is average variable cost increasing, constant, or decreasing? What about average total cost?
a. To find the marginal cost, we need to determine how much the total cost increases when an additional worker is hired. The marginal cost is the change in total cost divided by the change in output. In this case, the change in output is 12 units and the change in total cost is $60 (since the wage rate is $60 per worker).
So, the marginal cost is $60/12 = $5.
b. The average variable cost is the total variable cost divided by the total output. In this case, the variable input is labor, and the total variable cost is the wage rate per worker multiplied by the number of workers. The wage rate is $60 and the number of workers is 20, so the total variable cost is $60 × 20 = $1200.
Since the average product of labor is 30, the average variable cost is $1200/30 = $40.
c. The average product of labor is the total output divided by the number of workers. In this case, the total output is not provided. However, we know that the average product of labor is 30 and the last worker added 12 units to the total output. So, the total output must be (30 × 19) + 12 = 588 units.
d. The average total cost is the total cost divided by the total output. In this case, the total cost includes both fixed cost and variable cost. Given that the fixed cost is $3,600 and the variable cost is $1200, the total cost is $3600 + $1200 = $4800.
The total output is 588 units, so the average total cost is $4800/588 ≈ $8.16 (rounded to two decimal places).
e. To determine whether average variable cost is increasing, constant, or decreasing, we need to compare it to the average product of labor. Since the average product of labor is 30 and the average variable cost is $40, it means that the average variable cost is increasing because it is greater than the average product of labor.
As for the average total cost, it is the sum of average fixed cost and average variable cost. Since the average fixed cost is constant at $3,600/20 = $180 and the average variable cost is increasing, it means that the average total cost is also increasing.
f. To determine if ABC publishing is making a rational decision, we need to consider the marginal product of labor (MPL) and the marginal product of a press (MPP). The last printer added 20 books to total output and the last press added 1,000 books to total output.
The MPL for the last printer is 20 and the MPP for the last press is 1,000.
To evaluate the rationality of the decision, we need to compare the extra cost of hiring the last printer and the extra benefit of hiring the last press.
The extra cost of hiring the last printer would be an additional wage cost of $20 (assuming the wage rate for all printers is the same).
The extra benefit of hiring the last press would be an additional 1,000 books to the total output.
If the additional benefit from hiring the last press (1,000 books) outweighs the additional cost of hiring the last printer ($20), then the decision is rational. However, without knowing the price of books and other costs, we cannot determine if the decision is rational.
To find the answers to these questions, we need to understand the concepts of marginal cost, average variable cost, output production, average total cost, and the rationality of a decision. Let's go through each question one by one, explaining how to get the answers.
a. Marginal cost (MC) is the additional cost incurred by producing one extra unit of output. In this case, the last worker added 12 units to total output at a wage rate of $60. To calculate marginal cost, divide the change in total cost by the change in output. Since we know the wage rate and the additional output, we can calculate MC.
b. Average variable cost (AVC) is the variable cost per unit of output. To find AVC, divide the total variable cost (which is the wage rate multiplied by the number of workers) by the total output. Since we are given the wage rate and the number of workers, we can calculate AVC.
c. Output production refers to the total quantity of goods or services produced by a firm. In this case, we are not given the specific output quantity directly. However, we know that the average product of labor is 30 and the last worker added 12 units to the total output. From this information, we can calculate the total output.
d. Average total cost (ATC) is the total cost divided by the quantity of output produced. To find ATC, we need to determine the total cost. We know the fixed cost is $3,600, and we can calculate the variable cost using the wage rate and the number of workers. By adding the fixed cost and the variable cost, we get the total cost. Then, dividing the total cost by the quantity of output, we can calculate ATC.
e. To determine if the average variable cost (AVC) is increasing, constant, or decreasing, we need to compare it with the marginal cost (MC). If MC is lower than AVC, then AVC is decreasing. If MC is higher than AVC, then AVC is increasing. If MC is equal to AVC, then AVC is constant. For average total cost (ATC), we can use the same logic.
f. To assess the rationality of the decision made by ABC publishing, we need to compare the marginal product of labor (MPL) with the wage rate and the marginal product of the capital (MPK) with the price of the printing press. If the additional output gained from hiring the last worker (MPL multiplied by the wage rate) is greater or equal to the additional output gained from buying the last printing press (MPK multiplied by the price of the press), then the decision is rational. Otherwise, it may not be rational.
By following these explanations, you can calculate the values and determine whether the publisher's decision is rational.