Consider a firm that must determine not only the price at which to sell its goods, but also the associated level of advertising expenditure. At a given price, an increase in advertising will raise sales. Let the demand for the goods produced by this firm is given by = 10, 000 where −5 1/2 is the quantity produced, is the price, and is the advertising expenditure. The production cost of this firm is = 0. 8. 1. Write down this firm’s optimization problem. 2. Write down the first order derivative conditions. 3. Write down the second order derivative conditions, and check whether they are satisfied. 4. Calculate the optimal price, output and advertising expenditure ?
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Answer:
A perfectly competitive firm has only one major decision to make—namely, what quantity to produce. To understand why this is so, consider the basic definition of profit:
Since a perfectly competitive firm must accept the price for its output as determined by the product’s market demand and supply, it cannot choose the price it charges. Rather, the perfectly competitive firm can choose to sell any quantity of output at exactly the same price. This implies that the firm faces a perfectly elastic demand curve for its product: buyers are willing to buy any number of units of output from the firm at the market price. When the perfectly competitive firm chooses what quantity to produce, then this quantity—along with the prices prevailing in the market for output and inputs—will determine the firm’s total revenue, total costs, and ultimately, level of profits.
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