Why does getting more output from each additional worker translate into lower costs for each additional unit of output?
Whenever a firm produces a good, it has various kinds of costs. It has fixed costs (the building, the machinery) and it has variable costs (materials that get used up in making the goods and labor).
If a firm can increase its productivity (get more output from each worker in a given amount of time), the cost of each unit of output goes down. That's because the amount of money the firm paid the worker per good produced dropped.
So think of it this way. If I pay you $10 an hour and you make 10 t-shirts my costs are lower than if I pay you $10 and you make 20 t-shirts.
There are several ways you can answer this questions. However, the easiest way to address it is by saying if the total cost structure has an embedded fixed cost component, then the more units produced lowers the fixed cost associated with each unit.
Think of total cost as being comprised of fixed cost and variable cost. Variable cost stays the same per unit no matter how many units are produced. However, fixed cost gets lower, per unit, the more units there are to divide the cost by.
The question makes an assumption that getting more output from additional workers, or in other words, increase in manpower, always results in lower cost for additional output,. This assumption is not always true. There are several component costs of the total cost. These include among others labour, material and equipment usage cost. There is no guarantee that sum of these unit production costs for these inputs for additional production achieved from additional workers will be less than the average unit cost of existing production. As a matter of fact even the average unit cost of labour need not be lower.
It will be reasonable to assume that additional production from additional workers will result in lower unit cost for additional production, only when we assume that the production facility has a fixed cost and is currently producing below the maximum production capacity. In this case the unit cost of additional production is lower because the fixed cost gets divided over larger number of units produced.
It should be noted that it is possible that unit variable cost may increase with production, and in this way offset the benefits of apportioning fixed costs over a larger production quantity.