Suppose that a firm is currently employing 10 workers, the only variable input, at a wage rate of $100. The average physical product of labor is 25, the last worker added 10 units to total output, and total fixed cost is $5,000.
a. What is marginal cost?
b. What is average variable cost?
c. How much output is being produced?
d. What is the average total cost?
e. Is average variable cost increasing, constant, or decreasing?
Please let me know if I am on the right track?
a) The firm paid the last hired worker $100 and he produced 10 units. So, cost of producing the last unit (MC) is 100/10 = $10
b) The firm hires 10 workers and pays them $100 each, so Total variable costs are 10*100 = 1000. On average, a worker makes 25 units, so total units are 25*30 = 750. So, the average variable cost of producing a unit (AVC) is = 1000/750 = 1.33.
c) 750 from b)
d) Total fixed costs are total variable costs (1000) plus total fixed costs (given at $5000). So, TC = 5000+1000 = 6000. Average total costs = TC/Q = 6000/750 =8.
e) Since the marginal (last) worker added 10 unit and the overall average is 25 units, average variable costs must be rising. If AVC is rising, TVC must also be rising.
To answer these questions, we need to understand the concepts of marginal cost, average variable cost, output, and average total cost. Let's break down the calculation for each question:
a. Marginal cost (MC) represents the additional cost incurred when producing one more unit of output. To calculate marginal cost, we need to determine the change in total cost when producing one more unit of output.
In this scenario, we are given that the last worker added 10 units to total output. Therefore, to find marginal cost, we divide the change in total cost by the change in total output:
Marginal Cost = Change in Total Cost / Change in Total Output
b. Average variable cost (AVC) refers to the variable cost per unit of output. To calculate average variable cost, we divide the total variable cost by the total output:
Average Variable Cost = Total Variable Cost / Total Output
c. The output produced by the firm can be determined by the average physical product of labor. In this scenario, it is given that the average physical product of labor is 25 units. This means that, on average, each worker produces 25 units of output.
d. Average total cost (ATC) represents the total cost per unit of output. To calculate average total cost, we divide the sum of total fixed cost (TFC) and total variable cost (TVC) by the total output:
Average Total Cost = (Total Fixed Cost + Total Variable Cost) / Total Output
e. To determine if average variable cost is increasing, decreasing, or constant, we need additional information or data points indicating cost changes at different levels of output.
Now, let's plug in the given information and perform the calculations to find the answers to these questions.
a. To find the marginal cost, we need to divide the change in total cost by the change in output. The last worker added 10 units to total output and the wage rate is $100, so the change in total cost is $100 * 10 = $1000. Therefore, the marginal cost is $1000.
b. The average variable cost is the variable cost per unit of output. To find it, we need to divide the total variable cost by the output. The total variable cost is the wage rate multiplied by the number of workers, which is $100 * 10 = $1000. The output is not given in the question, so we cannot calculate the average variable cost without that information.
c. The output is not given in the question, so we cannot determine the exact quantity being produced.
d. The average total cost is the total cost divided by the output. Total cost is the sum of fixed cost and variable cost. The fixed cost is given as $5000, and the variable cost is the wage rate multiplied by the number of workers, which is $100 * 10 = $1000. Therefore, the total cost is $5000 + $1000 = $6000. Since the output is not given, we cannot calculate the average total cost without that information.
e. Without knowing the output and the corresponding variable costs at different levels of output, we cannot determine whether the average variable cost is increasing, constant, or decreasing.