Final answer:
To identify the minimum price for a firm to earn a profit in a perfectly competitive market, we need to find the output level where MR equals MC. With only the total cost function provided and no revenue details, we can't specify a minimum price without additional market price data.
Step-by-step explanation:
The minimum price (p) for the firm to earn a profit in a perfectly competitive market can be determined by analyzing the total cost function (tc = 100 - 4q²). A firm maximizes profit at the level of output where marginal revenue (MR) equals marginal cost (MC), and as per the given reference, this occurs at Q = 80. However, without information on the actual market price or the revenue function, we cannot calculate a specific minimum price.
For a perfectly competitive firm, the profit is calculated using the equation (Price)(Quantity produced) - (Average cost)(Quantity produced). Since this type of firm acts as a price taker, it will set its production level where its marginal cost equals the market price.
For example, if at a quantity of 40, the market price is $16 and lies above the firm’s average cost, the firm would earn economic profits, calculated as total revenue ($640, if selling at $16 per unit) minus total cost ($580). The profit here would be $60, represented by the shaded area above the average cost curve on a profit diagram.