Michael K. answered • 01/08/20
PhD Economist with 10+ years of teaching experience
Some things to start:
Let's assume Labor is the only variable input. That is, there are no other additional costs to produce each additional unit listed in the table (otherwise there is insufficient information to answer this question). Let's also remember that profit maximization (the goal of a firm) occurs when Marginal Cost (MC) equals Marginal Revenue (MR). So we need to find the MC and MR in this situation. I've pasted in a table below with the original numbers given in the question and some additional calculations explained as we go.
Marginal Revenue is given directly. It's the additional revenue for each additional unit sold -- that's just the price! So MR = $5.
Marginal Cost is a little more difficult. We need to know how much output is added for each additional unit of labor (called the marginal product of labor or MPL). This is just the change in the total output column here. The first worker adds 14 units to production since no units were produced before adding a worker. The second worker adds 12 units to production (26 minus 14). The third worker adds 11 units (37 minus 26), and so on. Then we just need to know how much this additional output is costing the firm (that's marginal cost!). To do this, divide the wage ($40 or $50 dollars) by the MPL. Doing this, we see that each additional unit of output from the first worker costs the firm $2.87; each additional unit of output from the second worker costs the firm, $3.33, and so on.
The last step is to see when MC=MR. They won't be exactly equal, but we can see that if wage is $40, MC is less than MR for labor up to 4 workers, so it makes sense to hire 4 workers. The 5th worker costs the firm more to hire then the additional revenue the worker generates. If wage is $50, then it makes sense to hire 3 workers following the same logic.
