Suppose that you supply bottled water in a competitive market and that you are producing the profit-maximizing quantity of bottled water. If you can sell your water at $2 a bottle and you currently employ five workers at a wage of $50 a day, what is the value of the marginal product of the last worker you hired? What is the marginal product of that worker?
To calculate the value of the marginal product of the last worker hired, you need to determine the additional revenue generated from the additional output produced by that worker.
To find this, follow these steps:
Step 1: Determine the profit-maximizing quantity of bottled water. This can be done by equating the marginal cost (MC) to the marginal revenue (MR). If the marginal cost is less than the marginal revenue, you should continue to produce more, and if the marginal cost is greater than the marginal revenue, you should produce less.
Step 2: Once you have determined the profit-maximizing quantity, find the total revenue (TR) at that quantity. In this case, the price per bottle is $2. So, if you can sell your water at $2 a bottle, the total revenue will be the selling price multiplied by the quantity.
Step 3: Calculate the total cost (TC) at the profit-maximizing quantity. To find the total cost, multiply the wage per worker by the total number of workers. In this case, the wage per worker is $50, and the total number of workers is five.
Step 4: Subtract the total cost from the total revenue to derive the profit (π). Profit is given by the formula π = TR - TC.
Step 5: Determine the additional profit generated from the additional output produced by the last worker hired. To do this, compare the profit at the profit-maximizing quantity (π_1) to the profit when one more worker is added (π_2). The difference between these two profit levels represents the additional profit generated by the last worker.
The marginal product of the last worker hired is equal to the additional profit divided by the additional output generated by that worker. So, divide the additional profit by the additional quantity of output produced to find the value of the marginal product.
Finally, to answer the question about the marginal product of that worker, it is equal to the additional quantity of output generated by that worker when compared to the previous level of output.
Please note that without specific data provided on the relationship between the number of workers and the quantity of bottled water produced, it is not possible to give a concrete answer to the value of the marginal product and marginal product of the last worker hired in this scenario.