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?
To answer these questions, we need to understand a few concepts related to production and cost:
1. Marginal Cost (MC): This is the additional cost incurred by producing one more unit of output. It is calculated by dividing the change in total cost by the change in quantity.
MC = (Change in Total Cost) / (Change in Quantity)
2. Average Variable Cost (AVC): This is the variable cost per unit of output. It is calculated by dividing the total variable cost by the quantity of output.
AVC = Total Variable Cost / Quantity
3. Output: The quantity of goods produced.
4. Average Total Cost (ATC): This is the average cost per unit of output. It is calculated by dividing the total cost (fixed cost + variable cost) by the quantity of output.
ATC = (Total Fixed Cost + Total Variable Cost) / Quantity
Now let's answer the questions using the given information:
a. To find the marginal cost, we need to know the change in total cost and the change in quantity. However, we are not given this information directly. So we will use the definition of marginal cost: the last worker added 10 units to total output. As we are given the average physical product of labor (25), we can deduce that the previous quantity of output with 9 workers was 9 * 25 = 225. So the change in quantity is 10 (from the last worker). As for the change in total cost, we are not given the information. Therefore, we cannot determine the exact marginal cost.
b. Average Variable Cost (AVC) is calculated by dividing the total variable cost by the quantity of output. However, we are not given the total variable cost, so we cannot calculate the average variable cost.
c. No information is provided about the quantity of output being produced, so we cannot determine it.
d. Average Total Cost (ATC) is calculated by dividing the total cost (fixed cost + variable cost) by the quantity of output. Given that the fixed cost is $5,000, we cannot calculate the total variable cost or the quantity of output; hence, we cannot determine the average total cost.
e. Since we cannot calculate the average variable cost or determine the change in average variable cost at different levels of output, we cannot determine if it is increasing, constant, or decreasing.
In summary, without additional information about the change in total cost, total variable cost, and quantity of output, we are unable to answer questions a, b, c, d, and e accurately.