ECON 2300 Lecture Notes - Lecture 17: Marginal Revenue, Price Discrimination, Maxima And Minima

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amaranthhamster412

6 Feb 2017

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Recall that this means that the monopolist sells to different people at different prices, but every unit of the good sold to a given group is sold at the same price. Third-degree price discrimination is the most common form of price discrimination. Examples of this might be student discounts at the movies, or senior citizens" discounts at the drugstore. Let us suppose that the monopolist is able to identify two groups of people and can sell an item to each group at a different price. We suppose that the consumers in each market are not able to resell the good. Let us use p1(y1) and p2(y2) to denote the inverse demand curves of groups 1 and 2, respectively, and let c(y1 + y2) be the cost of producing output. Then the profit-maximization problem facing the monopolist is max y1,y2 p1(y1)y1 + p2(y2)y2 c(y1 + y2). The optimal solution must have mr1(y1) = mc(y1 + y2) mr2(y2) = mc(y1 + y2).

Related Questions

3rd degree price discrimination. We have the same market conditions as the previous problem. p1(q1) = 1, 000 â q1 p2(q2) = 500 â q2 This producer also faces a constant marginal cost of 100.

i. If the monopolist is able to effectively conduct 3rd degree price discrimination, what are the optimal price-quantity pairs for each group of consumers?

ii. What is the total CS, PS, and W from both markets?

iii. If the monopolist can only charge a single price, what are the optimal output and price?

iv. How much is sold to each type of consumer?

v. Find the CS, PS, and W for this scenario.

vi. Compare the three welfare measures in the two scenarios.

harlequinwombat678

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?

purplehound509

1. Danny's Dump Truck sells its output in both the domestic and the foreign markets. Because of import and export restrictions, there is not possibility of a purchase in one market that could then be sold in the other market. The demand function associated with each market is as follows:

P₁ = 20,000 - 2Q₁ P₂ = 25,000 - 50Q₂

Danny's marginal cost is $10,000 in both markets. (assume AC= MC) Suppose the firm can engage in third degree price discrimination.

a. Find the price and output in each market. Find Danny's total profits through price discrimination.

b. Graphically show how Danny charges different prices in different markets.

c. Calculate the price elasticity of demand for each market.

lavenderarmadillo497

ECON 2300 Lecture Notes - Lecture 17: Marginal Revenue, Price Discrimination, Maxima And Minima

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