1. Define Q to be the level of output produced and sold, and assume that the firm's cost function is given by the relationship
TC = 20 + 5Q + Q2
Furthermore,assume that the demand for the output ofthe firm is a function of price P given by the relationship
Q = 25 -P
a. Define total profit as the difference between total revenue and total cost, express in terms ofQthe total profit function for the firm.(Note: Total revenue equals price per unit times the number ofunits sold.)
b. Determine the output level where total profits are maximized.
c. Calculate total profits and selling price at the profit-maximizing output level.
d. If fixed costs increase from $20 to $25 in the total cost relationship,determine the effects ofsuch an increase on the profit-maximizing output level and total profits.
2. Using the cost and demand functions in Exercise 5:
a. Determine the marginal revenue and marginal cost functions.
b. Show that,at the profit-maximizing output level determined in part (b) of Exercise 5,marginal revenue equals marginal cost.This illustrates the economic principle that profits are maximized at the output level where marginal revenue equals marginal cost.