PERFECT COMPETITION

IN-CLASS WORKSHEET 4

This question examines a perfectly competitive firm in the market for soap. You will use the market equilibrium price and firm-specific cost functions to identify the profit-maximizing output of a perfectly competitive firm and examine whether market entry or exit is likely.

Sam's Soap is one of many producers in the perfectly competitive soap market. Sam's Soap is a price-taking firm, and the equilibrium market price for a bar of soap is $3. Suppose that the marginal cost of producing soap at Sam's Soap is MC = Q/10, where Q is the number of bars of soap that the firm produces.

Task 1: Identify the profit-maximizing number of soap bars that Sam's Soap should produce.

Task 2: When Sam's Soap produces the profit-maximizing number of soap bars, how much total revenue does it earn?

Task 3: Suppose the total cost Sam's Soaps incurs can be expressed as TC = 205 + Q²/20, where Q is the number of bars of soap that the firm produces. When Sam's Soap produces the profit-maximizing number of soap bars, how much total cost does it incur?

Task 4: Suppose the total cost Sam's Soaps incurs can be expressed as TC = 205 + Q²/20, where Q is the number of bars of soap that the firm produces. When Sam's Soap produces the profit-maximizing number of soap bars, how much profit does it earn?

Task 5: Based on your answers above, would you expect new firms to enter the perfectly competitive market, or would you expect some existing firms to exit? Explain your answer carefully.