There are two groups of customers in the market. Demand of group number 1 is Q1(p)...

There are two groups of customers in the market. Demand of group number 1 is Q1(p) = 3−0.5p, and demand of group number 2 is Q2(p) = 5−2p. The market is served by a monopolist with MC = 1. (a) Write down the market demand function (remember that demand function should be welldefined for all possible prices). Plot it. (b) Derive the MR(Q) for the market demand and plot it on the graph from above. (c) What price will the monopolist charge if she cannot price discriminate? Find the corresponding consumer surpluses for both groups. (d) Now suppose that the monopolist can set different prices for different groups. What prices will she choose? Find the corresponding consumer surpluses for both groups. (e) Who wins and who loses when discrimination is allowed? How does total welfare change?

Solutions

Expert Solution

Question

Answer : Qm = Market Demand

For a straight line demand curve, its Marginal Revenue curve is a straight line bisector of demand curve.

A monopolist always operate with elastic demand markets.

Part A :

Market demand is the sum pf all individual demand curve horizontally.

Part B :

MR = Marginal Revenue, it is the first order derivative of total revenue

Part C :

Consumer surplus = 1/2 * Quantity * difference in price

Part D :

Part E :

when discrimination is allowed, monopolist start operating in both markets, charging a higher price in inelastic market and a slightly lower price in elastic market. Hence, profits of monopolist rises

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

A firm sells its product to two groups of customers. Demand from group 1 is Q1...

A firm sells its product to two groups of customers. Demand from group 1 is Q1 = 100, 000− 5,000P and demand from group 2 is Q2 = 140,000 − 10,000P. a) Find the total demand that the firm faces for its product. Explain it first using pictures, and then do the algebra. Write your answer of the total demand as quantity as a function of price. (Hint: draw pictures. Then add the two demands horizontally; that is, at each...

Consider a monopolist facing two groups of consumers with demand curves given by q1= 5−p and...

Consider a monopolist facing two groups of consumers with demand curves given by q1= 5−p and q2= 5−2p. The monopolist does not have any cost of production. (a) Find the profit-maximizing prices and quantities under third-degree price discrimination (group-specific pricing) (b) If the monopolist cannot price discriminate (must charge everyone the same price), what is the demand curve facing the firm? (Hint: remember to sum demand curves horizontally) (c) Find the profit-maximizing price and quantity for the monopolist who does...

Q1.Two firms produce in a market with demand P=100-Q. The marginal cost for firm 1 is...

Q1.Two firms produce in a market with demand P=100-Q. The marginal cost for firm 1 is constant and equals 10. The marginal cost of firm 2 is also constant and it equals 25. Firm 1 sets output first. After observing firm 1's output, firm 2 sets its output. (Please pay attention. Read the brackets correctly.) 1a. For firm 2, the best response is R₂(q₁)=(A-q₁)/2. The value for A is? 1b. Solve for the Stackelberg equilibrium. The quantity sold by firm...

Assume two firms 1 and 2. The inverse market demand function is given by: P=30-(q1+q2)...

Assume two firms 1 and 2. The inverse market demand function is given by: P=30-(q1+q2) Each firm produces with marginal costs of MC = 6 Fixed costs are zero. The next questions refer to the Cournot duopoly. Question 1 (1 point) What is Firm 1's total revenue function? Question 1 options: TR1=30q1 -q1 -q22 TR1=30-2q1-q2 TR1=30q1 -q12-q2 None of the above. Question 2 (1 point) What is Firm 1's marginal revenue function? Question 2 options: MR1=30-2q1 -q2 MR1=30-q1-2q2 MR1=30-2q1-2q2...

1. Suppose we have two consumers in the market. Joe has the following demand curve: P=10-Q1....

1. Suppose we have two consumers in the market. Joe has the following demand curve: P=10-Q1. Lucy has the following demand curve: P=10-3Q2. Find (algebraically) the formula for the market (or aggregate) demand curve. Draw all 3 curves on 3 separate graphs that should be drawn next to each other (so I can see the horizontal summation of quantities).

1. If a firm has two groups of customers whose elasticities of demand are different, how...

1. If a firm has two groups of customers whose elasticities of demand are different, how does it determine what prices to charge each group? a. Sets the price (P) equal to marginal revenue (MR) equal to marginal cost (MC) in each market. b. Sets the MR in each market equal to the firm’s MC and sets the price for each group by finding the prices on each group’s demand curve above where MR=MC. c. Sets MC equal to P...

Q1: Demand in a market is represented by Q = 500 – 50P where P is...

Q1: Demand in a market is represented by Q = 500 – 50P where P is measured in dollars per unit and Q is measured in units per week. Note: Demand in this question is identical to that in Q1 of Assignment #10. a) Complete the following table. Find elasticity between $10 and $8, between $8 and $6, between $6 and $4, between $4 and $2, and between $2 and $0. Show elasticity to two decimal places. Do not round...

Suppose a monopolist faces two groups of consumers. Group 1 has a demand given by P1...

Suppose a monopolist faces two groups of consumers. Group 1 has a demand given by P1 = 50−2Q1 and MR1 = 50−4Q1. Group 2 has a demand given by P2 = 40−Q2 and MR2 = 40−2Q2. The monopolist faces MC=AVC=ATC=$10 regardless of which group she supplies to. We can infer from the demand equations that in equilibrium Group __ is the inelastic group because the elasticity at that point is __ in absolute value than that of the other group....

In market 1, let demand be given by q1 = A−5p. In market 2, let demand...

In market 1, let demand be given by q1 = A−5p. In market 2, let demand be given by q2 = 500−10p. Let Q = q1 + q2. Let total costs be C(Q) = 20 + 2Q. Let A < 250. If a monopolist is forced to charge the same price in both markets what price will that be? What is the price in each market if the monopolist can charge different prices in each market? As a consumer in...

2. A firm is operated under monopoly where there are two groups of customers. The market...

2. A firm is operated under monopoly where there are two groups of customers. The market demand from group 1 is given by Q1 = 80 – P. The market demand from group 2 is given by Q2 = 40 – P/2. The firm’s marginal cost function is given by MC =20. a. Total market demand is given by Q= Q1 + Q2 = 120 – 3P/2. Find the firm’s producer surplus from combining the two markets and set a...

Subjects