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 $5000. The last printer added 20 books to total output, while the last press added 1000 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

Well, it seems like the Largo Publishing House is having quite the bookish conundrum! Let's delve into this matter, shall we?

To determine whether the publishing house is making the optimal input choice, we need to consider their marginal productivity and costs.

First, let's look at the printers. The last printer added 20 books to the total output. Considering their wage rate of $20, this means that each additional book produced by the last printer costs $1 (20 books / $20 wage rate = $1 per book).

Now, let's analyze the printing presses. The last press added 1000 books to the total output. Given the cost of a printing press at $5000, this means that each additional book produced by the last press costs $5 (1000 books / $5000 press cost = $5 per book).

Comparing the costs, we see that the cost per book for the last printer is $1, while for the last press, it's $5. Therefore, it appears that the publishing house is not making the optimal input choice.

To adjust input usage, the manager of Largo Publishing House should consider reducing the number of printing presses and increasing the number of printers. By doing so, they can decrease the cost per book and achieve a more efficient production process.

Remember, the goal is to find the perfect balance between productivity and cost-efficiency. And with that, good luck to the manager of the Largo Publishing House – may their input choices be as clever as a well-crafted pun!

To determine if the publishing house is making the optimal input choice, we need to compare the marginal productivity of both printers and printing presses with their respective costs.

The marginal productivity of a printer is the additional number of books produced by adding one more printer, which in this case is 20 books. The wage rate for a printer is $20. Therefore, the marginal productivity per dollar spent on a printer can be calculated as:

Marginal productivity per dollar spent on a printer = Marginal productivity of a printer / Wage rate for a printer
= 20 books / $20
= 1 book per dollar

The marginal productivity of a printing press is the additional number of books produced by adding one more printing press, which in this case is 1000 books. The cost of a printing press is $5000. Therefore, the marginal productivity per dollar spent on a printing press can be calculated as:

Marginal productivity per dollar spent on a printing press = Marginal productivity of a printing press / Cost of a printing press
= 1000 books / $5000
= 0.2 books per dollar

Comparing the marginal productivity per dollar spent on printers and printing presses, we can see that the marginal productivity per dollar spent on a printer is higher (1 book per dollar) than the marginal productivity per dollar spent on a printing press (0.2 books per dollar).

Since the publishing house wants to maximize output for a given level of input costs, it should allocate more resources towards the input with the higher marginal productivity per dollar spent. In this case, the manager of Largo Publishing House should adjust input usage by reducing the number of printing presses and increasing the number of printers.

By reallocating resources, the publishing house can increase its total output without increasing input costs, hence making a more optimal input choice.

To determine if the Largo Publishing House is making the optimal input choice, we need to consider its marginal productivity and costs.

The marginal productivity of each input, in this case, printers and printing presses, can be measured by the additional output generated when one more unit of that input is added.

For the printers, the marginal productivity is given as an increase of 20 books when the last printer was added. So, the marginal productivity of the printers is 20 books.

For the printing presses, the marginal productivity is given as an increase of 1000 books when the last press was added. So, the marginal productivity of the printing presses is 1000 books.

To assess cost efficiency, we need to compare the marginal productivity with the cost of each input. The wage rate for a printer is $20, and the price of a printing press is $5000.

The marginal cost of hiring a printer is $20 since that is the wage rate. Similarly, the marginal cost of adding a printing press is $5000 since that is the purchase price.

To determine if the publishing house is making the optimal input choice, we need to compare the marginal productivity to the marginal cost.

For the printers, the marginal productivity is 20 books at a cost of $20, resulting in a marginal productivity-to-cost ratio of 20/20 or 1.

For the printing presses, the marginal productivity is 1000 books at a cost of $5000, resulting in a marginal productivity-to-cost ratio of 1000/5000 or 0.2.

Ideally, the Largo Publishing House should allocate resources in such a way that the marginal productivity-to-cost ratio is the same for all inputs. In this case, the ratio for printers is 1, while the ratio for printing presses is 0.2. This indicates that the publishing house is not making the optimal input choice.

To adjust input usage, the manager of Largo Publishing House should allocate resources in a way that equalizes the marginal productivity-to-cost ratios. Since the ratio for printers is higher, it suggests that hiring more printers would be more cost-effective compared to adding additional printing presses. By hiring more printers, the manager can increase output more efficiently and reduce overall costs.

In summary, the publishing house is not making the optimal input choice as the marginal productivity-to-cost ratios differ. The manager should adjust input usage by hiring more printers to achieve a balance in productivity and costs.