A firm has two factories, one twice as large as the second. As the number of workers at each factory increases, which factory will experience diminishing returns first?

The smaller of the two factories will begin to see diminishing returns first. That is because they will have exhausted the capacity of the fixed factor of production(i.e. the factory) sooner. In other words, production will reach its maximum level because the factory only has the capacity for X output so returns will dwindle with each additional input of labor.

To determine which factory will experience diminishing returns first as the number of workers increases, we need to understand the concept of diminishing returns and apply it to each factory.

Diminishing returns is a principle in economics that states that as more and more of a variable input (in this case, workers) is added to a fixed input (such as factory size), the marginal productivity of the variable input will eventually start to decrease.

Let's denote the number of workers at the first factory as W1 and at the second factory as W2. Since the first factory is twice as large as the second, we can assume that the second factory has a fixed input, so the only variable input is the number of workers.

Now, let's analyze each factory separately:

1. First Factory:
As the number of workers, W1, increases, the total output can initially increase at an increasing rate due to economies of scale. However, at some point, adding more workers will lead to diminishing returns. This could happen when the factory starts to face resource constraints, such as limited space or machinery, which restrict the efficiency of additional workers.

2. Second Factory:
Since the second factory is smaller and has a fixed size, it may reach its resource constraints sooner. As the number of workers, W2, increases, the factory may quickly reach its maximum capacity, causing diminishing returns to set in earlier compared to the first factory.

Therefore, in this scenario, the second factory, which is smaller in size, is more likely to experience diminishing returns first as the number of workers increases.

To determine which factory will experience diminishing returns first, we need to understand the concept of diminishing returns. Diminishing returns occur when increasing one input while holding other inputs constant leads to a proportionally smaller increase in output.

In this case, we have two factories, one twice as large as the second. Let's call the size of the smaller factory "x" and the larger factory "2x". Assuming all other factors are held constant, we can compare the two factories as the number of workers increases.

Diminishing returns occur when the marginal productivity of an additional worker declines. Marginal productivity refers to the increase in output generated by each additional worker.

Assuming both factories have the same efficiency, it is likely that the larger factory (2x) will experience diminishing returns first. This is because as the number of workers increases, the larger factory will reach its capacity (2x) sooner compared to the smaller factory (x).

Essentially, the larger factory will require more workers to reach its full capacity, and once it reaches its capacity, adding more workers may result in diminishing returns as there is limited space or resources for them to be productive.

However, it's important to note that this is a general analysis and other factors such as technology, resource availability, and management practices can also influence the occurrence of diminishing returns.