Question

In: Economics

2. A monopoly with constant marginal costs of $10 can sell to two groups of potential...

2. A monopoly with constant marginal costs of $10 can sell to two groups of potential consumers, with demands Q1=100-p, Q2=100-2p respectively.

a. Find the optimal price-quantity combination in each market if the firm is able to price-discriminate. (10 pts)

b. Find the consumer surplus for group 1 and group 2 with price discrimination. (5 pts)

c. Find the optimal price-quantity combination if the firm is not able to price-discriminate. (10 pts)

d. Find the consumer surplus for group 1 and group 2 without price discrimination. (5 pts)

Expert Solution

2. A monopoly with constant marginal costs of $10 can sell to two groups of potential consumers, with demands Q1=100-p, Q2=100-2p respectively. Inverse demand functions are P1 = 100 - Q1 and P1 = 50 - 0.5Q1

This implies the respective marginal revenues are

TR1 = P1Q1 = 100Q1 - Q1^2..........MR1 = 100 - 2Q1

TR2 = P2Q2 = 50Q2 - 0.5Q2^2 ......MR2 = 50 - Q2

Combined demand is Q = 100 - P + 100 - 2P or Q = 200 - 3P. Inverse demand is P = 200/3 - Q/3. MR = 200/3 - 2Q/3.

a. Find the optimal price-quantity combination in each market if the firm is able to price-discriminate.

In that case, it will charge different prices according to MR = MC rule

MR1 = MC and MR2 = MC

100 - 2Q1 = 10 and 50 - Q2 = 10

This gives Q1 = 90/2 = 45 units and Q2 = 40 units

Prices are P1 = 100 - 45 = $55 and P2 = 50 - 0.5*40 = $30.

b. Find the consumer surplus for group 1 and group 2 with price discrimination.

CS = 0.5*(max price - current price)*qty

CS1 = 0.5*(100 - 55)*45 = 1012.50

CS2 = 0.5*(50 - 30)*40 = 400

c. Find the optimal price-quantity combination if the firm is not able to price-discriminate.

Firm will charge a single price

MR = MC

200/3 - 2Q/3 = 10

Q = 85 units and P = 200/3 - 85/3 = $38.33

Q1 = 100 - 38.33 = 61.67 units and Q2 = 100 - 2*38.33 = 23.34 units

d. Find the consumer surplus for group 1 and group 2 without price discrimination.

CS1 = 0.5*(100 - 38.33)*61.67 = 1901.60

CS2 = 0.5*(100 - 38.33)*23.34 = 719.68

Rahul Sunny answered 2 years ago

A monopoly with constant marginal cost mc=$20 has two potential groups of customers, whose demands are...

A monopoly with constant marginal cost mc=$20 has two potential groups of customers, whose demands are Q1=100-.8p and Q2 =125-p, respectively. Fixed cost is 0. a) If the firm knows the type of each individual consumer, and it can charge two two-part tariffs, what are these two two-part tariffs under first degree price discrimination? b) If the monopoly can charge them the same two-part tariff, and unit price is equal to marginal cost, what is the fixed fee the monopolist...

A monopoly has a marginal cost of zero and faces two groups of consumers. At first,...

A monopoly has a marginal cost of zero and faces two groups of consumers. At first, the monopoly could not prevent resale, so it maximized its profit by charging everyone the same price,p = $5. No one from the first group chose to purchase. Now the monopoly can prevent resale, so it decides to price discriminate. Will total output expand? Why or why not? What happens to profit and consumer surplus?

Your firm A is a monopoly in a particular market. You can produce at constant marginal...

Your firm A is a monopoly in a particular market. You can produce at constant marginal cost of $50 for every additional unit you produce. You have avoidable fixed costs of $6,000 per year. You face a market demand curve given by Q = 540 – 2P, where Q is the number of units sold per year, and P is the price per unit. a. What is the equation of your marginal revenue curve? b. What is your firm’s profit-maximizing...

Suppose a monopoly can produce any level of output it wishes at a constant marginal (and...

Suppose a monopoly can produce any level of output it wishes at a constant marginal (and average) cost of $5 per unit. Assume the monopoly sells its goods in two different markets separated by some distance. The demand curve in the two markets are given by FIRM1 : Q1 = 55 − P1 FIRM2 : Q2 = 70 − 2P a) How would your answer change if it costs demanders only $5 to transport goods between the two markets? What...

Suppose a monopoly has constant marginal costs of $20 per unit. Demand for the monopolist’s product...

Suppose a monopoly has constant marginal costs of $20 per unit. Demand for the monopolist’s product is Q = 100 - P. Please show the work to receive the full credit. i. What are the profit maximizing price and quantity for this monopoly? ii. How many units of the product would the competitive market supply? What would the equilibrium price be? iii. Calculate how much consumer surplus would be lost if this market started off as perfectly competitive but then...

Suppose a textbook monopoly can produce any level of output it wishes at a constant marginal...

Suppose a textbook monopoly can produce any level of output it wishes at a constant marginal (and average) cost of $5 per book. Assume that the monopoly sells its books in two different markets that are separated by some distance. The demand curve in the first market is given by Q_1=55- P_1 and the curve in the second market is given by Q_2=70-2P_2 Remember sometimes is easier to work with inverse demand functions. First assume that the monopolist can charge...

A company has monopoly rights to sell the popular video “Boyfights”. Suppose there are two groups...

A company has monopoly rights to sell the popular video “Boyfights”. Suppose there are two groups of buyers of Boyfights. Demand for the respective groups is given by the following equations: Group I: P1 = 10 – Q1 Group II: P2 = 8 – 2Q2 Where Q1 and Q2 are the number of Boyfights movies sold to each group. The total cost function for making each copy of the movie is TC = Q, where Q = Q1 + Q2....

Two firms compete under Cournot competition with constant marginal costs c1 = 2 and c2 =...

Two firms compete under Cournot competition with constant marginal costs c1 = 2 and c2 = 4. The market demand is P=18-Q . a) Compute the market share of each firm, the market price, and the total quantity produced in the market. b) [CHALLENGING] You later hear that the marginal cost of firm 2 increased, and realize that the market price is now P = 9. What is the new marginal cost c2 ?

Suppose a monopoly with constant marginal cost of 10 sells its product to identical consumers. Each...

Suppose a monopoly with constant marginal cost of 10 sells its product to identical consumers. Each consumer has an inverse demand curve given by P = 210 − 10Q. (a) Find the price and quantity the monopolist chooses if it can only set one price, and it can not use a two-part tariff. What is the monopolist’s profit on each consumer? (b) Now suppose the monopolist can use a two-part tariff. What is the profit maximizing choice of the fixed...

4. A monopolist can produce at constant average and marginal costs of AC = MC =...

4. A monopolist can produce at constant average and marginal costs of AC = MC = 10. The firm faces a market demand curve given by P = 100 - Q. (a) Calculate the profit-maximizing level of output and price for the monopolist. Also calculate the monopolist's profit. (b) Assume this industry suddenly becomes perfectly competitive. Calculate the price and industry output if this industry is perfectly competitive. (c) Calculate the deadweight welfare loss that the monopoly in (a) imposes...