Q. A survey of households in a small town showed that in 850 of 1,200 sampled households, at least one member attended a town meeting during the year. Using the 99% level of confidence, what is the confidence interval for the proportion of households represented at a town meeting?
1. My Big Banana (MBB) has a monopoly in Middletown on large banana splits. The demand for this delicacy is given by Q = 80 - P. MBB's costs are given by TC = 40 + 2Q + 2Q2. What is the maximum monopoly profit?
2. A firm under monopolistic competition faces the demand curve: P = 500 - 12.5Q. The firm's marginal cost is MC = 200 + 5Q.
a. Find the firm's profit-maximizing output and price.
b. Assuming that the firm is at its long-run equilibrium position, estimate total revenue, total cost, and total profit.
3. A monopolist faces the demand curve: P = 8,400 - 3Q, and has long-run average cost LAC = 900 - 3Q + Q2.
a. Derive equations for revenue, marginal revenue, total cost, and marginal cost.
b. Determine the monopolist's profit-maximizing output, price, and profit.
4. Industry demand for a good is given by: P = 60 - .5Q. The industry's long-run cost is $10 per unit: LAC = LMC = $10.
a. A monopolist controls the industry. Find its output and price.
b. Instead, suppose that the same industry is perfectly competitive. Find the long-run equilibrium price and output. Comment on the differences between the monopoly and competitive results.
5. A 5-member commodity cartel faces the demand curve: P = 60 - .4Q. Each member can produce output at (constant) LAC = LMC = $20 per unit.
a. Describe how the cartel should operate to maximize its total group profit.
b. Under the group profit-maximizing cartel agreement in part a, one member produces 10 units of output. It is tempted to secretly increase its output to 20 units. Assess this strategy and comment on cartel stability.