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Suppose you are the proprietor of the only bar in Dallas. Since you are the only place in town for people to get drinks you exercise some market power and face a downward sloping demand curve for drinks given by P = 10 - (3/2)Q for each individual. Your total costs are given by TC = Q. There are 100 individuals with identical demand.

  1. Assuming that you must follow a uniform pricing strategy, what is the profit maximizing price and quantity and the associated profit? What is consumer surplus? Is the market efficient?
  2. If each person is charged their reservation price, what type of price discrimination is this? Assuming you can engage in this pricing scheme, what is your profit maximizing price and quantity and the associated profit? What is consumer surplus? Is the market efficient?
  3. Now assume that you decide to try a two-part tariff scheme instead, charging a price per drink and a cover charge at the door. What is the optimal two-part tariff charged to each person? How many drinks will be sold to each person? What is your total profit associated with this scheme? What is the total consumer surplus? Is the market efficient?
  4. Assume that your clientele is composed of two types: 50 customers are heavy drinkers with individual demand described by P_H = 15 - Q_H and 50 customers are light drinkers with individual demand described by P_L = 10 -3Q_L. Which group would you rather charge a higher price? Why?
  5. Assume that the market is split as described before. There is no constraint on the number of drinks you can sell. You can charge a different price to each group. What is the optimal price and corresponding quantity for each segment of the market? What is your total profit under this scheme? What type of price discrimination is this?
  6. Assume that the market is split as described before. The city of Dallas tells you that can only sell 325 drinks in total. You can charge a different price to each group. What is the optimal price and corresponding quantity for each segment of the market? What is your total profit under this scheme?

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Related questions

3. A monopolist has two sets of customers. The inverse demand for Group 1 is described by P1 = 200 - Q1. For Group 2, the inverse demand is P2 = 100- Q2. The monopolist faces ca constant marginal cost of 40. Let Q be the aggregate quantity demanded.

a. (10 points) Show that the monopolist's total demand if the two markets are treated as one is: Q=0; P =200

Q=200-P;100<P =200
Q=300-2P;0<P = 100
b. (10 points) Show that the monopolist's profit-maximizing price is P = 95 if both groups are to be charged the same price. At this price, how much is sold to members of Group 1 and how much

to members of Group 2? What is the consumer surplus of each group? What are the total profits?

4. Now suppose that the monopolist in problem #3 can separate the two groups and charge separate, profit-maximizing prices to each group.

a. (10 points) What will these prices be? What is consumer surplus? What are the total profits?
b. (10 points) If the total surplus is consumer surplus plus profit, how has price discrimination affected total surplus?

Use your knowledge about price-searching firms and two-part pricing to advise the company below. A company has a bar and is trying to decide on the cover charge (if any) and price for each drink. It has done a modest regression study in which it asked customers to classify themselves as light drinkers or heavy drinkers and to indicate the number of drinks they would typically consume during the evening. The estimate from the regression study is that a change in the price equal to $1 per drink causes light drinkers to change their consumption on average by 0.5 drinks per night. However, a change in the price of $1 causes heavy drinkers to change their consumption on average by 1.0 drinks per night. For both groups, a typical consumer will not consume anything once the price reaches $9 per drink. (They may instead go to another bar or not go to a bar at all.) Draw a demand curve for a typical light drinker and for a typical heavy drinker on the same diagram. Explain your diagram. Write equations for the curves in slope-intercept form.

If 300 people visit the bar on a typical evening, with 200 people being light drinkers and 100 people being heavy drinkers, draw an overall demand curve for all of the consumers combined. What is the slope and what is the intercept for this demand curve? Write an equation in slope-intercept form. If the marginal cost of making drinks (the alcohol, the bartender's labor, and the amortized cost of purchasing glasses and cleaning them repeatedly) is constant at $5 per drink, and if no cover charge is assessed, what is the best price to charge for drinks? How many drinks would be sold on a typical evening? What would your profits be? If you cut your price by $1 per drink and assess the maximum possible cover charge without causing a typical light drinker to refuse to enter the bar, would your profits improve? How high would the cover charge be? Calculate both the cover charge and your total profits. Would the new pricing increase profit?

Maybe the best price cut is not exactly $1. Write a profit equation. Profits equal to total revenue minus total cost. Total cost equals $5 times the number of drinks sold. Total revenue equals the price for drinks times the number of drinks sold, plus 300 people times the cover charge. The cover charge equals, for a light drinker, the triangle of consumer surplus above the price but below the demand curve for a light drinker. (The area of a triangle equals one half the base times the height.) You will take the derivative of the profit equation with respect to P or Q and set it equal to zero. For example, use the equation for the total demand curve and solve for Q in terms of P. Then in the profit equation substitute in an expression involving P in place of every Q that was in the original profit equation. Now you can take a derivative of profits with respect to P and set the derivative equal to zero. Eventually, you can solve for the exact best P, Q, and cover charge.

Review of the slope-intercept form: Y= a - bX; a = the intercept on the Y-axis and b = the absolute value of the slope (slope=(change in Y)/(change in X)) For a demand curve: P=a-b Q. The intercept on the vertical axis would indicate a price that is so high that the quantity demanded becomes zero. The slope is the ratio of a change in price divided by the change in quantity demanded; the extra credit problem gives you information to determine the slope for a light drinker and the slope for a heavy drinker.

Question 1

The amount of profit that can be achieved using uniform pricing is __________ the profit that can be achieved from price discrimination because of _______.

Select one:

a. greater than; the cost of trying to determine every single consumer's individual demand (willingness to pay) is prohibitively expensive.

b. less than; uniform pricing is more costly so the ATC and AVC curves are higher than they are under price discrimination.

c. equal to; the TR and TC curves are equivalent under either pricing scheme, so there is no profit advantage to either scheme.

d. less than; total demand includes people who would be willing to pay more than, as well as less than, the uniform market price.

Question 2

A firm selling in two markets is practicing price discrimination:

Select one:

a. when it refuses to sell the good to some group of consumers.

b. anytime it charges different consumers different prices.

c. when it charges the same price to different consumers as long as they differ in their demand for the good.

d. when it is charging different consumers, different prices, and the price difference is not based upon cost differences.

Question 3

To successfully practice price discrimination:

Select one:

a. consumers in two separate markets must have identical demand.

b. the firm must possess market power.

c. it must be easy for consumers in one market to sell to consumers in the other market.

d. the firm must be a pure monopoly.

Question 4

If it could practice first-degree price discrimination, a firm with market power could earn:

Select one:

a. its typical monopoly profit as well as the area which, under uniform pricing, would represent the deadweight loss associated with market power.

b. an area half the size of its monopoly power under uniform pricing.

c. its typical monopoly profit as well as the area which, under uniform pricing, would represent consumer surplus.

d. its typical monopoly profit as well as the area which, under uniform pricing, would represent consumer surplus and the deadweight loss associated with market power.

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