the largo publishing house use 400 printers and 200 printers presses to produce book. a printers wage rate is 20 and the price of a printing press is 5000. the last printer added 20 books to total output. is the publishing house making the optimal in put 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 consider the marginal product of labor and capital.
First, let's calculate the marginal product of labor (MPL) and the marginal product of capital (MPK).
MPL = ΔQ / ΔL
where ΔQ is the change in total output and ΔL is the change in the number of labor inputs.
MPK = ΔQ / ΔK
where ΔK is the change in the number of capital inputs.
Given that the last printer added 20 books to the total output, we can assume ΔQ = 20.
Now, let's calculate MPL:
MPL = ΔQ / ΔL = 20 / (400 - 200) = 20 / 200 = 0.1
Next, let's calculate MPK:
MPK = ΔQ / ΔK = 20 / 1 = 20
To determine if the publishing house is making the optimal input choice, we need to compare the ratio of the marginal products to the ratio of input prices. The ratio of MPL to the wage rate is:
MPL / Wage rate = 0.1 / 20 = 0.005
The ratio of MPK to the price of a printing press is:
MPK / Price of printing press = 20 / 5000 = 0.004
Since MPL / Wage rate > MPK / Price of printing press, the publishing house is not making the optimal input choice. The marginal productivity of labor is higher relative to the cost of labor compared to the marginal productivity of capital relative to the cost of a printing press.
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 would help to achieve a better balance between the marginal productivity of labor and capital. By doing so, they can optimize their input choices and maximize their output.
To determine whether the publishing house is making the optimal input choice, we need to consider the marginal productivity and cost.
1. Marginal Productivity: The marginal productivity of an input is the additional output produced by using one more unit of that input. In this case, the last printer added 20 books to the total output.
2. Marginal Cost: The marginal cost is the additional cost incurred by using one more unit of an input. In this case, the cost of an additional printer is $5000.
Now, let's evaluate the situation:
The publishing house currently employs 400 printers and 200 printing presses. The marginal productivity of the last printer is 20 books, which means that by adding one more printer, the total output increased by 20 books.
The cost of an additional printer is $5000. Since the wage rate for a printer is $20, the publishing house spends $20*400 = $8000 on printers' wages. Therefore, adding one more printer would increase the wage cost by $20.
To determine whether the publishing house is making an optimal input choice, we compare the additional benefit (marginal productivity) with the additional cost (marginal cost).
In this case, the marginal benefit is the increase in output from adding one more printer (20 books), and the marginal cost is the additional cost of hiring one more printer ($5000).
If the marginal benefit is greater than the marginal cost, then it is optimal to add one more printer. However, if the marginal benefit is lower than the marginal cost, then the publishing house is not making the optimal input choice.
Based on the given information, we cannot determine whether 20 books of additional output justify the cost of $5000 for a new printer. We would need information about the price of each book and the demand for books to determine the profitability.
If the publishing house is not making the optimal input choice, the manager could consider alternative adjustments. For example, they could analyze the productivity and cost of using printing presses more efficiently, hiring additional staff, investing in technology automation, or optimizing the current printing process.