The Largo Publishing House uses 400 printers and 200 printing presses to produce books. A printer's wage rate is $20, and a printing press costs $5,000. The last printer added 20 books to total output, while the last press added 1,000 books to total output. Is the publishing house making the optimal input choice? Why or why not? If not, how should the manager of Largo Publishing House adjust input usage?
To determine if the Largo Publishing House is making the optimal input choice, we need to compare the marginal products of the printers and printing presses to their costs.
The marginal product of a resource is the additional output generated by employing one more unit of that resource.
First, let's calculate the marginal product of the last printer and last press:
Marginal product of the last printer = additional books produced / additional printers
= 20 books / 1 printer
= 20 books per printer
Marginal product of the last press = additional books produced / additional presses
= 1000 books / 1 press
= 1000 books per press
Next, let's compare the marginal products to their costs:
Cost per unit of printer = printer's wage rate = $20
Cost per unit of press = printing press cost = $5,000
Comparing the marginal product of the last printer (20 books per printer) to its cost ($20), we can see that the marginal product is higher than the cost. This indicates that the publishing house could benefit from employing more printers. Adding more printers would increase output at a lower cost.
On the other hand, comparing the marginal product of the last press (1000 books per press) to its cost ($5000), we can see that the marginal product is lower than the cost. This indicates that the publishing house may not be making the optimal use of printing presses. Adding more printing presses would increase output but at a higher cost.
Therefore, the manager of Largo Publishing House should adjust input usage by hiring more printers and potentially reducing the number of printing presses to achieve optimal input choice. By employing more printers, they can increase output at a lower cost. However, they should evaluate the marginal product and cost relationship of each additional input unit to determine the optimal mix of resources for their specific production needs.
To determine if the Largo Publishing House is making the optimal input choice, we need to compare the marginal product of each input (printers and printing presses) to the cost of employing additional units of that input.
The marginal product is the additional output generated by each additional unit of input. In this case, we have information about the marginal product of the last printer and the last printing press. The last printer added 20 books to the total output, while the last press added 1,000 books to the total output.
To determine if the publishing house is making the optimal input choice, we need to compare these marginal products to the costs associated with employing additional units of printers and printing presses.
Let's start with printers:
- The wage rate for a printer is $20 per hour.
- The marginal product of the last printer is 20 books.
To calculate the marginal cost of the last printer, we can divide the wage rate by the marginal product:
Marginal cost of the last printer = $20 / 20 books = $1 per book.
Next, let's consider printing presses:
- The cost of a printing press is $5,000.
- The marginal product of the last press is 1,000 books.
To calculate the marginal cost of the last press, we can divide the cost of the press by the marginal product:
Marginal cost of the last press = $5,000 / 1,000 books = $5 per book.
Comparing the marginal costs, we can see that the marginal cost of using an additional printer ($1 per book) is lower than the marginal cost of using an additional printing press ($5 per book).
Therefore, the publishing house is not making the optimal input choice. They should adjust their input usage by employing more printers and fewer printing presses.
By reallocating resources, the publishing house can reduce its costs and increase its productivity. They should hire more printers, as the marginal cost of printers is lower than that of printing presses. This means that employing additional printers results in a lower cost per book produced.
In summary, to make an optimal input choice, the publishing house should adjust input usage by hiring more printers and reducing the number of printing presses. This will help them achieve higher efficiency and minimize costs.