4. Assume a monopoly faces an inverse demand function of p = 150 - 3Q, and...

4. Assume a monopoly faces an inverse demand function of p = 150 - 3Q, and has a constant marginal and average cost of 30.

a. If the monopolist can perfectly discriminate, what is its profit, consumer surplus and total surplus, and what is the deadweight loss of monopoly?

b. If the firm is a single-price monopolist, what is its profit, consumer surplus and total surplus, and what is the deadweight loss of monopoly?

Solutions

Expert Solution

a) when there is perfect price discrimination the demand curve intersects the marginal cost curve which determine the lowest price offered and the total quantity served. This is because each consumer is charged his or her reservation prices

P = MC

150 - 3Q = 30

Q = 120/3 = 40 units

Consumer surplus = 0

Producer surplus = Profit = 0.5*(150 - 30)*40 = $2400

Total surplus = $2400

DWL = $0

b) Now MR = MC will determine the profit maximizing level of output

150 - 6Q = 30

Q = 120/6 = 20 units

Price P = 150 - 3*20 = $90

Consumer surplus = 0.5*(150 - 90)*20 = $600

Producer surplus = Profit = (90-30)*20 = $1200

Total surplus = 900 + 1200 = $2100

DWL = 0.5*(90-30)*(40-20) = $600

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

The inverse demand function a monopoly faces is P = 100 − Q. The firm’s cost...

The inverse demand function a monopoly faces is P = 100 − Q. The firm’s cost curve isTC(Q) = 10 + 5Q.Suppose instead that the industry is perfectly competitive. The industry demand curve and firm cost function is same as given before. (j) (4 points) What is the level of output produced? Compare it to the output of single price monopoly. (k) (4 points) What is the equilibrium price for this industry? Compare it to the price charged of single...

Assume a monopolist faces a market demand curve P = 190 - 3Q and has the...

Assume a monopolist faces a market demand curve P = 190 - 3Q and has the short-run total cost function C = 540 + 10Q. What is the profit-maximizing level of output? What are profits? Graph the marginal revenue, marginal cost, and demand curves, and show the area that represents deadweight loss on the graph. (Hint: derive the MR and MC functions and set MC=MR and solve). In Question 3 above, what would price and output be if the firm...

The inverse demand curve a monopoly faces is p = 100 - 2Q The firm's cost...

The inverse demand curve a monopoly faces is p = 100 - 2Q The firm's cost curve is C (Q) = 20 + 6Q What is the profit-maximizing solution? The profit-maximizing quantity is _______. (Round your answer to two decimal places.) The profit-maximizing price is $________. (Round your answer to two decimal places.) What is the firm's economic profit? The firm earns a profit of $________. (Round your answer to two decimal places.) How does your answer change if C(Q)...

. Suppose a monopoly faces inverse market demand P = 600 – 0.01Q, and that the firm’s...

. Suppose a monopoly faces inverse market demand P = 600 – 0.01Q, and that the firm’s total cost curve is C = 2,500,000 + 10Q + 0.015Q2. Find the firm’s profit-maximizing price and output PM, QMand sketch the equilibrium. Find the firm’s ATC formula. What is the ATC at the output level you found in part a? Add the ATC to your graph and indicate the firm’s profit. What is the total profit? What is the per unit profit at QM? Explain why...

A monopoly has an inverse demand function given by p = 120 - Q and a...

A monopoly has an inverse demand function given by p = 120 - Q and a constant marginal cost of 10. a) Graph the demand, marginal revenue, and marginal cost curves. b) Calculate the deadweight loss and indicate the area of the deadweight loss on the graph. c) If this monopolist were to practice perfect price discrimination, what would be the quantity produced? d) Calculate consumer surplus, producer surplus, and deadweight loss for this monopolist under perfect price discrimination.

Suppose that the incumbent firm faces an inverse demand function P = 110 − Q, and...

Suppose that the incumbent firm faces an inverse demand function P = 110 − Q, and has a constant marginal cost equal to 10. The potential entrant has a constant marginal cost equal to 10 and a fixed cost of 100. The incumbent firm first determines its quantity and commit to this amount. The potential entrant then determines whether it would enter and the quantity. Given that the entrant enters and the incumbent's quantity q1, the entrant's optimal strategy? What...

If a monopoly faces an inverse demand curve of p equals=390390minus−Q, has a constant marginal and...

If a monopoly faces an inverse demand curve of p equals=390390minus−Q, has a constant marginal and average cost of $30, and can perfectly price discriminate, what is its profit? What are the consumer surplus, welfare, and deadweight loss? How would these results change if the firm were a single-price monopoly?

A monopolist faces a demand of P = -3Q + 400. The monopolist’s marginal cost is...

A monopolist faces a demand of P = -3Q + 400. The monopolist’s marginal cost is MC = 2Q + 80. The total cost for the monopolist is TC = Q2 + 80Q + 6000 a) Find the profit-maximizing quantity, price, and profit of the monopolist. b) A regulatory agency tries to force the monopoly to produce the same quantity as a competitive firm. Show what this price and quantity is and why the firm will eventually shut down rather...

Suppose that a firm faces the demand curve, P = 100 - 3Q, where P denotes...

Suppose that a firm faces the demand curve, P = 100 - 3Q, where P denotes price in dollars and Q denotes total unit sales. The cost equation is TC = 200 + 22Q. a. Determine the firm’s profit-maximizing output and price. b. Suppose that there is a change in the production process so that the cost equation becomes TC = 80 + 12Q + Q2. Determine the resulting effect on the firm’s output: c. Using the two...

Consider a monopoly with inverse demand function p = 24 - y and cost function c( y) = 5...

Consider a monopoly with inverse demand function p = 24 - y and cost function c( y) = 5 y 2 + 4: i) Find the profit maximizing output and price, and calculate the monopolist's profits. ii) Now consider the case in which the monopolist has now another plant with the cost structure c 2( y 2) = 10 y 2. How much will the monopolist produce in each plant, what is the price, and the total profits of the monopoly? iii) Now suppose...

Subjects