When using 400 printers and 200 printing presses to produce books. A printer's wage rate is 20, and the price of printing press is 5,000. The last printer added 20 books to total, while the last press aded 1,000 books to total output. Is this an optimal choice?
In order to determine if this is an optimal choice, we first need to understand the concept of marginal productivity and marginal cost.
The marginal productivity of a resource is the additional output generated by adding one more unit of that resource. In this case, the marginal productivity of a printer is the additional number of books produced when one more printer is added, and the marginal productivity of a printing press is the additional number of books produced when one more press is added.
The marginal cost of a resource is the additional cost incurred by adding one more unit of that resource. In this case, the marginal cost of a printer is the wage rate, which is $20, and the marginal cost of a printing press is the price of the press, which is $5,000.
To determine if this is an optimal choice, we compare the marginal productivity with the marginal cost for both printers and presses.
For the last printer added, it produced an additional 20 books. Therefore, the marginal productivity of the last printer is 20.
For the last press added, it produced an additional 1,000 books. Therefore, the marginal productivity of the last press is 1,000.
Now, let's compare these marginal productivities with their respective marginal costs.
The marginal cost of a printer is $20, while the marginal productivity is 20 books. Therefore, the marginal productivity per unit of cost for a printer is 20/20 = 1.
The marginal cost of a press is $5,000, while the marginal productivity is 1,000 books. Therefore, the marginal productivity per unit of cost for a press is 1,000/5,000 = 0.2.
An optimal choice occurs when the marginal productivity per unit of cost is the same for all resources. In this case, the marginal productivity per unit of cost of a printer is 1, while the marginal productivity per unit of cost of a press is 0.2. Therefore, this is not an optimal choice, as the marginal productivity per unit of cost is different for printers and presses.
To make an optimal choice, you would want to compare the marginal productivity per unit of cost for printers and presses and allocate your resources in a way that maximizes this ratio. For example, if the marginal productivity per unit of cost of a printer is higher than that of a press, you might want to allocate more resources to printers and vice versa.
Note: This analysis assumes that all other factors affecting production are held constant and the decision is based solely on the given information about marginal productivity and marginal cost.