Calculate the consumer surplus that exists in market and

Question

Question 1. Suppose that Drexapparel gets a patent for a new type of t-shirt fabric that withstands any stains. As a monopolist in the market for this new type of shirt, Drexapparel faces market demand Q = 30 - p, where Q is in thousands of shirts and p is in dollars. Drexapparel's cost function for shirts is 50 + 0.5Q²

a. What is Drexapparel's inverse demand function? What is its revenue function? What is its marginal revenue function?

b. Determine the profit-maximizing quantity and price for Drexapparel's shirts given that the company is a monopolist in the market and sets a uniform price (i.e., a single price that it charges to all consumers).

c. On a graph with price p on the y-axis and quantity Q on the x-axis, draw the market demand curve, the marginal revenue curve, and the marginal cost curve. Using your figure, illustrate the profit-maximizing quantity and price you found in part (b).

d. What are Drexapparel's economic profits given its profit-maximizing choices of price and quantity?

e. Calculate the consumer surplus that exists in this market.

f. Calculate the producer surplus in this market. Does the producer surplus differ from firm profits? If so, why? If not, why not?

g. Calculate the deadweight loss that exists in this market.

h. Based on your answer to part (b), calculate the Lerner Index of market power. What is the elasticity of demand that Drexapparel faces?

i. Suppose that the government observes the high price being charged by Drexapparel for its t-shirts and decides to impose a price ceiling of $18 per shirt. If Drexapparel charges $18 per shirt, how many shirts will it sell? What are its economic profits in that case?

What is the deadweight loss in that case?

j. If the government wanted to completely eliminate the deadweight loss in this market, what should the price ceiling be? Using a new graph, explain your answer.

Question 2. Drexoogle has developed the first computer (the "earpod") that fits in one's ear and functions as a phone, can tell you the time, and will conduct Google searches all in response to a person's voice commands. Based on market research, Drexoogle has determined that the market demand for this product is Q = 500 - p, where Q is in thousands of earpods and p is in dollars. Drexoogle's cost function is 50Q.

First, suppose that Drexoogle can only set a uniform monopoly price for the earpod.

(a) What is the price and quantity that maximizes Drexoogle's economic profits?

(b) What are the economic profits that result from monopoly pricing?

(c) What is the consumer surplus and deadweight loss that result from monopoly pricing?

Now suppose that Drexoogle can perfectly price discriminate; that is, it can identify just by looking at a customer exactly what the maximum that customer would be willing to pay for the earpod.

(d) In this case, Drexoogle will not set a uniform price, but rather will set a different price for each customer based on their willingness to pay. What is the quantity of earpods Drexoogle should sell to maximize economic profits?

(e) What are the economic profits that result from perfect price discrimination?

(f) What is the consumer surplus and deadweight loss that result from perfect price discrimination?

Now suppose that Drexoogle cannot perfectly price discriminate, but can identify and separate two different groups of buyers in the market: students and business people (so total quantity Q = Q_students + Q_business). Students have demand that is given by Q_students = 380 - 0.8p.

Business people have demand that is given by Q_business = 120 - 0.2p.

(g) What is the price and quantity Drexoogle should set in the student market to maximize profits in that market? What is the price and quantity Drexoogle should set in the business people market to maximize profits in that market?

(h) What are the economic profits that result from demographic price discrimination?

(i) What is the consumer surplus and deadweight loss that result from demographic price discrimination?

3. Dragon Airlines knows that its customers consist of business travelers, whose demand for plane tickets over a 5-year period is given by Q_business = 100 - 0.2p, and leisure travelers, whose demand for plane tickets over a 5-year period is given by Q_leisure = 50 - 0.1p. Dragon Airlines' cost function is given by 100Q, where Q = Q_business + Q_leisure.  Assume for simplicity that there is only one business traveler and one leisure traveler in the market (the results you will find would generalize to any number of travelers, as long as they existed in equal proportions).

(a) Suppose that Dragon Airlines was interested in instituting a two-part tariff only for the business traveler in which it charges a 5-year membership fee for the right to purchase plane tickets from the company as well as a usage fee for each ticket purchased. What would be the profit-maximizing membership fee and the usage fee to charge the business traveler?

(b) What would be Dragon Airlines' economic profits if it only served the business traveler using the two-part tariff you solved for in part (a)?

(c) Show mathematically and explain in words why the leisure traveler would not be willing to pay the membership and usage fee you solved for in part (a).

(d) Solve for the profit-maximizing two-part tariff (i.e., the membership fee and usage fee) that both the leisure traveler and the business traveler would be willing to purchase.

(e) Putting both business and leisure travelers' demand curves in the same graph (with price on the y-axis and quantity on the x-axis), illustrate the two-part tariff you derived in part(d).

(f) What are Dragon Airlines' economic profits with the two-part tariff you derived in part

(d)? How do they compare to the economic profits Dragon Airlines earned from only serving business travelers with the two-part tariff you derived in part (a)?