market power alone does not guarantee high profits, since profits depend on the ratio of average costs to price. A firm may have more market power than another firm, but still make less profit. As an example, let's compare an average supermarket and a convenience store operating in the same area. In supermarkets, the margin is usually 15-20%, and in convenience stores 25-30 %. This is due to the fact that supermarkets operate in a more competitive environment — during their operation, other outlets are also working at the same time to ensure a significant number of customers, it is necessary to offer attractive prices. Convenience stores charge a higher price than supermarkets because some of their customers fall at a time when there is not a large selection of outlets or for the sake of a minor purchase, it makes no sense to look for other options. The number of visitors to such stores is generally less dependent on prices than in supermarkets (less elastic demand). According to the Lerner coefficient, small stores have more monopoly power because they charge higher margins on the same product. But at the same time, such stores usually receive a much smaller amount of profit than a supermarket, since they have a much smaller sales amount, and the average unit cost is higher. Derivation The Lerner Rule comes from the firm's profit maximization problem. A firm choosing quantity Q facing inverse demand curve P(Q) and incurring costs C(Q) has profit equalling revenue (where R = PQ) minus costs: Under suitable conditions (that this is a convex maximization problem, e.g. P(Q) and C(Q) are linear functions), we can find the maximum by taking the derivative of profit with respect to Q and getting the first-order-condition: which gives the standard rule of MR = MC. To get the Lerner Rule, switch to the notation dC/dQ = MC and rewrite as Divide by P to get using the derivative definition of elasticity. Examples Calculation Let's suppose we need to fill in the gaps in the following table: For L = -1/Ed and Ed = -1/L, the elasticity of demand for industry A will be -2.5. We can use the value of the Lerner index to calculate the marginal cost (MC) of a firm as follows: 0.4 = (10 – MC) ÷ 10 ⇒ MC = 10 − 4 = 6. The missing values for industry B