Problem 1: Apex, Inc. is a monopolist. The demand function for its product is estimated to be
Q = 60 - 0.4P + 6Y +2A
Where Q=quantity of units sold
P= price per unit
Y = per capita disposable personal income (thousands of dollars)
A = hundreds of dollars of advertising expenditures
The firm's average variable cost function is
AVC = Q2 - 10Q + 60 Y is equal to 3 (thousand) for the period being analyzed.
a. If fixed costs are equal to $1,000, derive the firm's total cost function and marginal cost function.
b. Derive a total revenue function and marginal revenue function for the firm.
c. Calculate the profit-maximizing level of price and output for Apex, Inc.
d. What profit or loss will Apex earn?
e. If fixed costs were $1,200, how would your answers change for parts a through d?
Problem 2: XYZ Mining, Inc. is a leading manufacturer of magnesium, which is used in many products, estimates the following demand schedule for its product:
Price ($/pound) Quantity (Pounds /Period)
Fixed costs of manufacturing chromium are $14,000 per period. The firm's variable cost schedule is as follows:
Output (Pounds /period) Variable Cost (per Pound)
a. Find the total revenue and marginal revenue schedules for the firm.
b. Determine the average total cost and marginal cost schedules for the firm.
c. What are the XYZ Mining's profit-maximizing price and output levels for the production and sale of magnesium?
d. What is XYZ Mining's profit (or loss) at the solution determined in part c?
The following covers various aspects of cost structures, revenue, and profit maximizing output decisions. Algebraic analysis is provided.