The following table shows the output of chairs produced by a firm at different units of capital rented. The price per chair is $10.

-Refer to the table above.If the price of a chair decreases to $5 and the rental price of machines is $50 per day,how many machines should the firm rent?

Question

The following table shows the output of chairs produced by a firm at different units of capital rented. The price per chair is $10.
 
-Refer to the table above.If the price of a chair decreases to $5 and the rental price of machines is $50 per day,how many machines should the firm rent?

Quizplus · Accepted Answer

To find out the optimal number of machines the firm should rent, we need to compare the marginal product of each additional unit of capital (i.e., machines) with the marginal cost of renting those machines. We can calculate the marginal product of capital by taking the difference in output between two adjacent levels of capital. For example, the marginal product of the 3rd unit of capital is 30 - 20 = 10 chairs.

| Units of Capital | Output (chairs) | Marginal Product |
|-----------------|----------------|------------------|
| 1               | 10             |        -          |
| 2               | 20             |       10          |
| 3               | 30             |       10          |
| 4               | 36             |        6          |
| 5               | 40             |        4          |
| 6               | 42             |        2          |
| 7               | 42             |        0          |

Next, we need to calculate the marginal cost of renting each unit of capital, which is simply the rental price per day. In this case, the rental price is $50 per day, regardless of how many machines are rented.

| Units of Capital | Marginal Cost |
|-----------------|---------------|
| 1               | $50           |
| 2               | $50           |
| 3               | $50           |
| 4               | $50           |
| 5               | $50           |
| 6               | $50           |
| 7               | $50           |

Finally, we can determine the optimal number of machines to rent by comparing the marginal product and marginal cost at each level of capital. The optimal level of capital is the one where the marginal product equals the marginal cost. In this case, this occurs at the 5th unit of capital, where the marginal product is 4 chairs and the marginal cost is $50. Therefore, the firm should rent 5 machines.

Note that the decrease in price from $10 to $5 does not affect the optimal level of capital, as this is determined solely by the marginal product and marginal cost.

The Following Table Shows the Output of Chairs Produced by a Firm