3 Utility regulation A monopolist utility has cost function $C(q) = 2\sqrt{q}$ and operates in a market with aggregate demand curve $D(p) = (p/3)^{-3/2}$. 1. Plot the demand curve and the firm's marginal revenue and marginal cost curves on a single graph. 2. Calculate the firm's optimal price and output if it acts as a monopolist in the market. Mark both of these numbers on your graph. What are its monopoly profits? 3. Calculate the output level which maximizes social surplus. Mark this number on your graph. What is the deadweight loss of monopoly in this market? Calculate it and shade in the corresponding region on your graph. 2 4. Suppose a regulator imposes a price ceiling $\bar{p}$ on the market. What is the lowest $\bar{p}$ the regulator can impose without shutting down the utility? Can the regulator achieve efficiency by imposing a price ceiling?
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The following graph describes the demand, marginal revenue, marginal cost, and average total cost curves that a monopolist faces. Use the graph to answer the questions below. 1. What will be the monopoly price, output, and profit for this firm? (3 points) 2. Shade the sections of the graph that represent the consumer surplus and producer surplus. (2 point) 3. If this industry were competitive and every firm had the same marginal costs shown in the picture, what would be the price, output and profit? (3 points) 4. Shade the section of the graph that represents the deadweight loss from the monopoly. (1 point)
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A monopolist operates with the following data on cost and demand. It has a total fixed cost of $1000 and a total variable cost of Q^2, where Q is the number of units of output it produces. The firm's demand function is Qd = 60-0.5p. The firm expects the conditions of demand and cost to continue in the foreseeable future. a) What is the inverse market demand curve? b) What is the marginal revenue function that corresponds to the market demand curve? c) What is the monopolist's marginal cost function? d) What is the firm's revenue if it operates and maximizes profit? e) What is the deadweight loss from the monopoly pricing? f) Should the firm continue to operate in the short run, or should it shut down?
Consider an industry with the demand curve $(D)$ and marginal cost curve $(M C)$ shown in the accompanying diagram. There is no fixed cost. If the industry is a single-price monopoly, the monopolist's marginal revenue curve would be $M R$. Answer the following questions by naming the appropriate points or areas. a. If the industry is perfectly competitive, what will be the total quantity produced? At what price? b. Which area reflects consumer surplus under perfect competition? c. If the industry is a single-price monopoly, what quantity will the monopolist produce? Which price will it charge? d. Which area reflects the single-price monopolist's profit? e. Which area reflects consumer surplus under single-price monopoly? f. Which area reflects the deadweight loss to society from single-price monopoly? g. If the monopolist can price-discriminate perfectly, what quantity will the perfectly pricediscriminating monopolist produce?
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