Consider the market for natural gas with the following market demand and market total-cost functions: D : P(Qd) = 120 - 0.02Qd; C(Qs) = 25,000 + 60Qs.Q is weekly production in cubic meters (m3), and P is price in cents per cubic meter (so is the cost function). Assuming the firm maximizes profit, answer the following questions.
Assume the natural-gas market is perfectly competitive.
i. What is the equilibrium market price and market quantity? Show your work.
ii. What is the total profit earned in this market? Show your work.
iii. What is the Lerner index for any firm operating in this perfectly-competitive market? Show your work. Hint: Price and marginal cost are evaluated at the equilibrium quantity.
iv. If future weekly profitability is the same as current weekly profitability, and each firm earns a fraction of weekly market profitability, will any firm stay in this market and provide natural gas? Explain.
Assume the natural-gas market is a monopoly.
v. What is the equilibrium market price and market quantity? Show your work.
vi. What is the total profit earned in this market (by the monopolist)? Show your work.
vii. What is the Lerner index for the monopolist? Show your work.
viii. How do you know from the Lerner index that the monopolist has a higher level of market power than the perfectly-competitive firm?
ix. If any natural-gas firm is allowed to operate as a monopolist, will it stay in this market and provide natural gas? Explain.
x. Draw the marginal cost, demand, and marginal revenue curves for this market (on same graph). Identify and label the areas associated with surplus transferred to the monopolistic firm from consumers, and deadweight-loss to producers and consumers. Make sure to label all lines and axes.
xi. How much welfare is transferred from consumers to the monopolist?
xii. How much welfare is “lost” due to the market being a monopoly instead of a perfectly-competitive market? Note, it is harder to argue this is “lost” welfare, as any welfare from the market existing is lost if no firm supplies the market
xiii. What is a natural monopoly?
xiv. Give two examples of current-day natural-monopoly industries, clarifying why you think they are natural monopolies (think of fixed costs).
xv. A firm that has the same individual cost function as the market cost function in this problem is a natural monopoly. How do you know?
xvi. Describe a policy solution that could induce a firm to supply the above naturalgas market yet while reducing the welfare loss from a monopoly.