Question

assume the firm is selling output in a perfectly competitive market, the price of the product is $2, total fixed costs are equal to $5 and the wage rate paid to workers is $7.50. the value of marginal product (vmp) of the third worker is equal to:

Answer 1

The value of the marginal product (VMP) for the third worker is calculated by multiplying the marginal product of labor by the product's price in the market. Without the exact marginal product of the third worker, we cannot determine the VMP but can infer it would be equal to or greater than the wage rate if the production level is similar to the provided example.

Step-by-step explanation:

The question is asking for the value of the marginal product (VMP) for the third worker in a firm that operates in a perfectly competitive market. To calculate the VMP, we multiply the marginal product of labor by the output price of the product. While the provided information does not give the exact marginal product of the third worker, we can infer based on the given example that if a worker can produce two widgets per hour and each widget sells for $4, making the VMP $8 per hour for that worker. In the student's context, since the price is $2 per unit, we would need to know how many units the third worker can produce to calculate the VMP accurately. However, from the example, we could surmise that if the third worker can produce at least 4 units per hour (similar to the example which gives us 2 units per hour at $4 each), then the VMP would be equal to or greater than the wage rate of $7.50.

Answer 2

Since the additional revenue generated by hiring the third worker is $0, the value of the marginal product (VMP) of the third worker is $0. This means that the firm would not gain any additional revenue from hiring the third worker.

In a perfectly competitive market, the value of the marginal product (VMP) of a worker is equal to the additional revenue generated by the firm from hiring an additional worker.

To find the VMP of the third worker, we need to compare the additional revenue generated by hiring the third worker with the wage rate paid to the workers.

In this case, the price of the product is $2, and the total fixed costs are $5. Let's calculate the additional revenue generated by hiring the third worker:

1. Calculate the total variable costs for three workers:
- For the first worker: Wage rate * 1 worker = $7.50 * 1 = $7.50
- For the second worker: Wage rate * 2 workers = $7.50 * 2 = $15
- For the third worker: Wage rate * 3 workers = $7.50 * 3 = $22.50

2. Calculate the total cost for three workers:
- Total cost = Total fixed costs + Total variable costs
- Total cost = $5 + ($7.50 + $15 + $22.50) = $5 + $45 = $50

3. Calculate the total revenue for three workers:
- Total revenue = Price * Quantity
- Total revenue = $2 * Quantity

4. Since the firm is selling output in a perfectly competitive market, the firm can sell as much quantity as it wants at the market price. Therefore, the quantity will depend on the price and not on the number of workers hired. So, the total revenue for three workers will be the same as the total revenue for any other number of workers.

5. Now, let's calculate the additional revenue generated by hiring the third worker:
- Additional revenue = Total revenue for three workers - Total revenue for two workers
- Additional revenue = Total revenue for any number of workers - Total revenue for two workers
- Additional revenue = $2 * Quantity - $2 * Quantity = $0