(Table: Workers and Output) Look at the table Workers and Output.After graduation you achieve your dream of opening your own art shop that specializes in selling mud statues.You pay $10 per day on a loan from your uncle, and you pay $10 per day to each of your workers (who make the mud statues).After careful study, you determine the production information in the table.How many workers should you hire to minimize your marginal costs?
A)two
B)three
C)four
D)five

Question

Quizplus · Accepted Answer

The marginal cost is the change in total cost divided by the change in output. In this case, the total cost is the sum of the loan payment and the wages paid to the workers. The output is the number of mud statues produced. The marginal cost is therefore:MC = (10 + 10w) / qwhere w is the number of workers and q is the output.To minimize the marginal cost, we need to find the value of w that minimizes the expression (10 + 10w) / q. We can do this by taking the derivative of the expression with respect to w and setting it equal to zero:d/dw [(10 + 10w) / q] = 010/q = 0This equation has no solution, which means that the marginal cost is minimized at the point where the derivative is undefined. This occurs when q = 0, which means that we should hire no workers. However, this is not a feasible solution, as we need to produce some mud statues in order to sell them.The next best solution is to hire one worker. This will give us an output of 10 mud statues per day, and a marginal cost of 10/10 = 1. If we hire two workers, the output will increase to 20 mud statues per day, but the marginal cost will also increase to 10/20 = 0.5. This is a lower marginal cost than when we hire one worker, so we should hire two workers.

(Table: Workers and Output) Look at the Table Workers and Output.After