Question

Troll Corporation sells dolls for \(\$ 10\) each in a market that is perfectly competitive. Increasing the number of workers from 100 to 101 would cause output to rise from 500 to 510 dolls per day. Troll should hire the 101 st worker only when the wage is a. \(\$ 100\) or less per day. b. more than \(\$ 100\) per day. c. \(\$ 5.10\) or less per day. d. none of the above.

Short answer

The correct answer is choice (a), hire the 101st worker for \(\$100\) or less per day.

Step-by-step solution

Calculate Marginal Product (MP)

The marginal product of the 101st worker can be calculated by finding the difference in the output before and after hiring the 101st worker. In this case, we have: \(MP =\) Output with 101 workers \(−\) Output with 100 workers \(MP = 510 − 500 = 10\) The marginal product of the 101st worker is 10 dolls per day.

Calculate Marginal Revenue Product (MRP)

Now, we need to calculate the marginal revenue product of the 101st worker. This can be found by multiplying the marginal product (MP) calculated above by the price per doll (\(\$10\)). We have: \(MRP = MP \times \)Price per doll \(MRP = 10 \times \$10 = \$100\) The marginal revenue product of the 101st worker is \(\$100\) per day.

Compare MRP with Wage Options

We know that firms should hire an additional worker if the MRP is greater than or equal to the wage paid. In this case, we can compare the MRP (\(\$100\)) with the wage options given in the choices: a. \(\$100\) or less per day b. more than \(\$100\) per day c. \(\$5.10\) or less per day Since the MRP is \(\$100\), Troll Corporation should hire the 101st worker when the wage is: a. \(\$100\) or less per day - This is the correct choice because the MRP is equal to the wage, meaning hiring the 101st worker will not decrease the firm's profits. The correct answer is choice (a), hire the 101st worker for \(\$100\) or less per day.

Key concepts

Marginal Product

Understanding the concept of marginal product (MP) is crucial for analyzing the productivity and contribution of additional workers in various production processes. MP refers to the additional output that is produced when one more unit of a variable input, typically labor, is added, holding all other inputs constant. Simplifying this concept, it can be thought of as the output that the 'next' worker will generate.

For instance, if a toy factory employs one more worker and production increases from 500 to 510 toys, the marginal product of that new worker is 10 toys per day. It is important to track marginal product because it informs business decisions, like determining the optimal number of employees. A rising MP indicates increased efficiency up to a certain point, after which it generally falls due to the law of diminishing returns. Hence, it is a pivotal measurement for firms looking to optimize their resources.

Perfectly Competitive Market

A perfectly competitive market is an idealized form of market structure that includes many sellers and buyers, with all firms selling an identical product. In this environment, individual firms have no control over the price of the product; they are said to be 'price takers' rather than 'price makers'.

Within such a market, the Troll Corporation, from our example, is one of many firms selling dolls. No single firm can influence the price of dolls; they must accept the market price set by the laws of supply and demand. For Troll Corporation, their product, dolls, would thus be sold at the going rate, which, in our scenario, is $10 per doll. Understanding this market structure is essential because it dictates how firms like Troll Corporation make strategic decisions about production and pricing. Firms aim to maximize profit by equating marginal revenue, which is the income from selling one additional unit, to marginal cost, which is the cost of producing that unit.

Firm Hiring Decision

When it comes to a firm's hiring decision in a perfectly competitive market, the concept of marginal revenue product (MRP) guides the decision-making process. This is a calculation of the additional revenue a firm expects to generate from hiring one more employee. It is essentially the product of the marginal product of labor and the price of the good or service produced.

In our case study of the Troll Corporation, calculating the MRP is a simple step that has profound implications. The firm should hire an additional worker if the MRP is equal to or greater than the worker's wage. If the MRP falls below the wage cost, hiring an extra worker is not profitable as it would lead to a decrease in overall profit. Thus, MRP serves as a critical determining factor in whether the firm should expand its workforce based on the assumed wage rate and contributes to strategic planning in staffing and production.