The Largo Publishing House 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 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?
Hiring a printer for $20 means getting 20 more books, or $1 per book. Adding a press for $5000 means getting 1000 books or $5 per book. Hmmmmm, What do you think the publisher should do??
should use more printers and fewer presses because printers cost less than presses.
To determine whether the publishing house is making the optimal input choice, we need to calculate the marginal product of labor and the marginal product of capital for both printers and printing presses.
The marginal product of labor (MPL) is the additional output produced when one additional unit of labor (printer) is added. In this case, the last printer added 20 books to the total output.
The marginal product of capital (MPK) is the additional output produced when one additional unit of capital (printing press) is added. In this case, the last press added 1,000 books to the total output.
To calculate MPL and MPK, we divide the additional output by the number of units added:
MPL = Additional output / Additional units of labor
MPK = Additional output / Additional units of capital
For printers:
MPL = 20 books / 1 printer = 20 books/printer
For printing presses:
MPK = 1,000 books / 1 press = 1,000 books/press
Now, let's compare the marginal product per dollar of each input. To do this, we need to calculate the marginal cost of labor (MCL) and the marginal cost of capital (MCK).
The marginal cost of labor (MCL) is the wage rate divided by the marginal product of labor:
MCL = Wage rate / MPL
MCL = $20 / 20 books/printer = $1 per book
The marginal cost of capital (MCK) is the price of the printing press divided by the marginal product of capital:
MCK = Price of press / MPK
MCK = $5,000 / 1,000 books/press = $5 per book
Now we can compare the marginal costs of labor and capital.
MCL ($1 per book) < MCK ($5 per book)
Since the marginal cost of labor is lower than the marginal cost of capital, the publishing house is not making the optimal input choice. The manager should adjust the input usage by decreasing the usage of printing presses (capital) and increasing the usage of printers (labor) to achieve a better cost-output ratio.
By reallocating resources from expensive printing presses to relatively cheaper printers, the publishing house can lower its production costs while maintaining or increasing total output. This adjustment can help the publishing house achieve an optimal input combination and maximize its profits.