Imagine that the efficient provision of telephone calls in a medium-sized city involves an initial investment of $100 million financed by borrowing at 6 percent and variable cost of 5 cents a phone call. The phone company's annual fixed cost would be $6.0 million (6.00 percent of $100).
A) Use this info about costs to plot marginal cost and average total cost.
B) Assume that regulators set price at 5 cents, the level of marginal cost. What is the firm's profit position if 60 million calls a year are demanded at that price?
C) Is setting price equal to marginal cost a viable option in this case? Why or why not?
A) To plot the marginal cost and average total cost, we need to understand the formulas for each.
Marginal Cost (MC) represents the additional cost incurred by producing one extra unit of output. In this case, the variable cost of 5 cents per phone call represents the marginal cost per unit.
Average Total Cost (ATC) represents the total cost per unit of output. It is calculated by dividing the total cost (fixed and variable) by the total quantity of output.
Now, let's plot the MC and ATC on a graph. The x-axis represents the quantity of phone calls, and the y-axis represents the cost (in dollars).
1. Marginal Cost (MC):
Since the variable cost is 5 cents per phone call, MC remains constant at 5 cents for all quantities. So, the MC curve will appear as a horizontal line at 5 cents on the y-axis.
2. Average Total Cost (ATC):
To calculate the ATC, we need to consider both the fixed cost and the variable cost. The formula for ATC is:
ATC = (Total Cost) / (Quantity of Output)
Given:
- Fixed cost = $6.0 million
- Variable cost = 5 cents per phone call
- Quantity of output = x (number of phone calls)
Total Cost = Fixed Cost + (Variable cost * Quantity of output)
Total Cost = $6.0 million + (0.05 * x)
ATC = ($6.0 million + (0.05 * x)) / x
For different quantities of output (x), calculate the ATC using the above formula. Plot these points on the graph, and connect them to form the ATC curve.
B) If regulators set the price equal to the marginal cost at 5 cents per phone call and 60 million calls are demanded at that price, we can calculate the firm's profit position.
Profit = Total Revenue - Total Cost
Total Cost = Fixed Cost + (Variable Cost * Quantity of Output)
Total Cost = $6.0 million + (0.05 * 60 million)
Total Revenue = Price per unit * Quantity of Output
Total Revenue = $0.05 * 60 million
Profit = ($0.05 * 60 million) - ($6.0 million + (0.05 * 60 million))
Calculate the profit using the above formula. If it is positive, the firm is making a profit. If it is negative, the firm is making a loss.
C) Setting the price equal to the marginal cost may not be a viable option in this case. When the price is set at 5 cents (equal to marginal cost) and 60 million calls are demanded, the firm's profit position will depend on the calculated profit in part B.
If the calculated profit is positive, the firm is making a profit, which means it may be a viable option. However, if the profit is negative, the firm is making a loss, indicating that setting the price equal to the marginal cost is not sustainable for the company.
In this case, additional factors such as the company's long-term viability, market competition, and potential for growth should be considered when deciding whether to set the price at marginal cost.