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 lat press added 1,00 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?

Take a shot. What do you think?

To determine whether the publishing house is making the optimal input choice, we need to compare the marginal product of each input to its respective input cost.

First, let's calculate the marginal product of the last printer and the last press:

Marginal product of the last printer = Increase in output / Increase in the number of printers
= 20 books / 1 printer
= 20 books per printer

Marginal product of the last press = Increase in output / Increase in the number of presses
= 100 books / 1 press
= 100 books per press

Next, let's calculate the productivity per dollar spent on each input:

Productivity per dollar of printers = Marginal product of the last printer / Wage rate of printers
= 20 books per printer / $20 per printer
= 1 book per dollar

Productivity per dollar of presses = Marginal product of the last press / Cost of a press
= 100 books per press / $5,000 per press
= 0.02 books per dollar

Comparing the productivity per dollar of the two inputs, we can see that the productivity per dollar of a printer is higher than that of a press. This indicates that the publishing house is not currently making the optimal input choice.

To adjust input usage, the manager of Largo Publishing House should reduce the number of printing presses and increase the number of printers. By reallocating resources in this way, they can increase productivity and make a more optimal input choice.

To determine if the publishing house is making the optimal input choice, we need to compare the marginal productivity of each input (printer and printing press) with their respective costs.

To calculate the marginal productivity of an input, we divide the change in output by the change in the quantity of that input. In this case, we can calculate the marginal product of the last printer by dividing the change in total output (20 books) by the change in the quantity of printers (1). Similarly, we can calculate the marginal product of the last printing press by dividing the change in total output (1,000 books) by the change in the quantity of printing presses (1).

Now let's calculate the marginal products:
Marginal product of the last printer = 20 books / 1 printer = 20 books per printer
Marginal product of the last printing press = 1,000 books / 1 printing press = 1,000 books per printing press

To compare costs, we need to consider the wage rate for printers ($20) and the price of a printing press ($5,000).

Now let's compare costs with marginal products:
Marginal product per dollar spent on printers = Marginal product of the last printer / Wage rate = 20 books per printer / $20 = 1 book per dollar
Marginal product per dollar spent on printing presses = Marginal product of the last printing press / Price of a printing press = 1,000 books per printing press / $5,000 = 0.2 books per dollar

Based on these calculations, we can see that the marginal product per dollar spent is higher for printers (1 book per dollar) compared to printing presses (0.2 books per dollar). This means that the publishing house is not making the optimal input choice. It would be more efficient to use more printers and reduce the number of printing presses.

To adjust input usage, the manager of Largo Publishing House should increase the number of printers and decrease the number of printing presses. By doing so, they can further maximize their output for a given cost. The exact adjustments will depend on the specific marginal product per dollar ratios and the desired level of output.