. 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?
The publisher paid $20 to a printer and got 20 books, or a $1 per book. He paid $5000 for a press and got 1000 books, or $5 per book. Sounds like he should get more printers and less presses.
To determine if the publishing house is making the optimal input choice, we can compare the marginal product of each input (printers and printing presses) with the ratio of their costs.
1. Marginal product of printers:
The fact that the last printer added 20 books to the total output indicates that the marginal product of printers is 20 books.
2. Marginal product of printing presses:
Similarly, the fact that the last press added 1,000 books to the total output suggests that the marginal product of printing presses is 1,000 books.
3. Cost ratio:
The cost ratio is calculated by dividing the cost of printers by the cost of printing presses. Let's calculate it:
Total cost of printers = Number of printers x Wage rate per printer
Total cost of printers = 400 x $20 = $8,000
Total cost of printing presses = Number of printing presses x Price per press
Total cost of printing presses = 200 x $5,000 = $1,000,000
Cost ratio = Total cost of printers / Total cost of printing presses
Cost ratio = $8,000 / $1,000,000
Cost ratio = 0.008
Now, let's analyze the results:
- The marginal product of printers (20 books) is smaller than the marginal product of printing presses (1,000 books).
- The cost ratio (0.008) indicates that printers are relatively cheaper than printing presses.
Based on these findings, it seems that the publishing house is not making the optimal input choice. The printing presses have a much higher marginal product compared to printers, which means they are producing a significant amount of output per unit used.
To adjust input usage, the manager of Largo Publishing House should consider reducing the number of printers and increasing the number of printing presses. This reallocation of resources will help the publishing house achieve a more optimal combination of inputs and maximize its overall output.
To determine whether the publishing house is making the optimal input choice, we can calculate the marginal product of labor (MPL) and the marginal product of capital (MPK).
The MPL is the change in total output resulting from adding one more unit of labor, in this case, one more printer. The MPK is the change in total output resulting from adding one more unit of capital, in this case, one more printing press.
To calculate the MPL and MPK, we need to use the information given:
- The number of printers is 400, and the last printer added 20 books to total output.
- The number of printing presses is 200, and the last press added 1,000 books to total output.
- The wage rate for printers is $20.
- The price of a printing press is $5,000.
To find the MPL, we divide the change in total output by the change in the number of printers:
MPL = Change in Total Output / Change in Number of Printers
MPL = 20 books / 1 printer = 20 books/printer
To find the MPK, we divide the change in total output by the change in the number of printing presses:
MPK = Change in Total Output / Change in Number of Printing Presses
MPK = 1,000 books / 1 press = 1,000 books/press
Now, let's compare the MPL and MPK with their respective costs:
Cost of Labor (CL) = Wage Rate * Number of Printers
CL = $20 * 400 = $8,000
Cost of Capital (CC) = Price of Printing Press * Number of Printing Presses
CC = $5,000 * 200 = $1,000,000
The publishing house is making the optimal input choice if the MPL divided by the wage rate (MPL/CL) is equal to the MPK divided by the cost of capital (MPK/CC).
MPL/CL = (20 books/printer) / $20 = 1 books/dollar
MPK/CC = (1,000 books/press) / $1,000,000 = 0.001 books/dollar
Based on these calculations, we can see that the publishing house is not making the optimal input choice. The MPL/CL ratio is significantly higher than the MPK/CC ratio.
To adjust input usage, the manager should hire more printing presses and reduce the number of printers. This will help achieve a better balance between the productivity gained from the inputs (books per dollar spent). By reallocating resources towards printing presses, the publishing house can increase its total output without substantially increasing costs.