Question

In: Economics

A monopolist has the cost function C(Q) = 30*Q, and faces two types of consumers, A...

A monopolist has the cost function C(Q) = 30*Q, and faces two types of consumers, A and B, with the following demand curves for its product:

PA = 60 – 3*QA

PB = 80 – 2*QB

  1. (4 points) What price will the monopolist charge under uniform pricing?
  2. (3 points) What prices will the monopolist charge if it can price discriminate?
  3. (3 points) How much higher is the monopolist’s profit in (b) than in (a)?

Solutions

Expert Solution

Given, C = 30Q

Differentiating TC wrt Q we get

MC = 30

and

A. When the firm charges uniform price then Pa = Pb and Qa + Qb = Q

Add the two equation we get

After simplifying we get the inverse demand function. As shown above. Now, calculate TR

Differentiate the TR wrt Q we get

Equate MR to MC

72 - 2.4Q = 30

=> 2.4Q = 72 - 30

=> Q = 42 / 2.4

=> Q = 17.5 units

P = 72 - 2.4 × 17.5 = $ 51

Profit = 51 × 17.5 - 30 × 17.5 = $ 367.50

b. The inverse demand function of A is

Equate it to MC

Now, calculating price

Revenue consumer A = 45 × 5 = $ 225

Now, calculating the quantity and price of consumer B

Equate MR to MC

Quantity consumer B = 12.5

Price = $ 55

Revenue from consumer B = 55 × 12.5 = $ 687.50

Profit from price discrimination

= TRa + TRb - TC

= 225 + 687.50 - 30 × 17.5

= $ 387.50

C. Difference in profit = 387.50 - 367.50 = $ 20.

Please contact if having any query will be obliged to you for your generous support. Your help mean a lot to me please help. Thank you

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

Consider a monopolist who has a cost function of ?(?)=???. This monopolist faces two consumers, the...
Consider a monopolist who has a cost function of ?(?)=???. This monopolist faces two consumers, the first having demand ??(??)=??−?? and the second having demand ??(??)=??−??. a) Calculate the profit-maximizing price and then the optimal quantity sold to each consumer under uniform pricing, i.e. the monopolist charges the same price for both consumers. What are the monopolist’s profits? b) Suppose now that the monopolist can engage in third degree price discrimination. Find the monopolists profit maximizing prices for consumers 1...
Consider a monopolist who has a cost function of ?(?)=???. This monopolist faces two consumers, the...
Consider a monopolist who has a cost function of ?(?)=???. This monopolist faces two consumers, the first having demand ??(??)=??−?? and the second having demand ??(??)=??−??. a) Calculate the profit-maximizing price and then the optimal quantity sold to each consumer under uniform pricing, i.e. the monopolist charges the same price for both consumers. What are the monopolist’s profits? b) Suppose now that the monopolist can engage in third degree price discrimination. Find the monopolists profit maximizing prices for consumers 1...
. A natural monopolist has the total cost function C(Q) = 500 + 5Q and faces...
. A natural monopolist has the total cost function C(Q) = 500 + 5Q and faces the inverse demand curve P = 100 – Q a) Find the monopolist’s price, quantity, profits, consumer surplus and deadweight loss if the monopolist is not constrained by a regulator (you probably want to draw a picture to help you answer CS and DWL) P = _________ Q = _________ π = _________ CS = ¬_________ DWL = _________ b) A regulator constrains the...
A monopolist has the following cost function: C(q) = 800 + 8*q + 6*q2 It faces...
A monopolist has the following cost function: C(q) = 800 + 8*q + 6*q2 It faces the following demand from consumers: P= 200 – 2*Q. There is another firm, with the same cost function, that may consider entering the industry. If it does, equilibrium price will be determined according to Cournot competition. How much should the monopolist optimally produce in order to deter entry by the potential entrant? How much would the monopolist produce if there were no threat of...
A monopolist with the cost function C(q) = q faces the market demand curve p =...
A monopolist with the cost function C(q) = q faces the market demand curve p = 101 -2q. What is the maximum amount the monopolist is willing to pay for advertising that shifts its demand curve to p = 101-q?
A monopolist faces a market demand: P = 200 – Q. The monopolist has cost function...
A monopolist faces a market demand: P = 200 – Q. The monopolist has cost function as C = 1000 + Q2, and marginal cost MC = 2Q. ( 1) Solve for Marginal Revenue (MR) function. (2) Find the profit-maximizing quantity? Profit? (3) Suppose the monopolist decides to practice 3rd degree price discrimination. Without solving for the 3rd degree price discrimination, can you compare the new profit earned by the monopolist with the old profit?
. A monopolist faces two types of consumers: low demand consumers and high demand consumers. A...
. A monopolist faces two types of consumers: low demand consumers and high demand consumers. A high demand consumer has valuation equal to VH(q) = 10 + q - q 2 for q units of output and a low demand consumer has valuation equal to VL(q) = 10 + q - 2q2 for q units of output. There are equal numbers of each type of consumer. Marginal cost of production is constant and equal to c. The monopolist wishes to...
A monopoly faces market demand Q = 30−P and has a cost function C(Q) = Q^2...
A monopoly faces market demand Q = 30−P and has a cost function C(Q) = Q^2 (a) Find the profit maximizing price and quantity and the resulting profit to the monopoly. (b) What is the socially optimal price? Calculate the deadweight loss (DWL) due to the monopolist behavior of this firm. Calculate consumer surplus (CS) and producer surplus (PS) given the profit maximizing price. (c) Assume that the government puts a price ceiling on the monopolist at P =22. How...
Question (Second-Degree Price Discrimination) A monopolist faces two types of consumers. The inverse demand function of...
Question (Second-Degree Price Discrimination) A monopolist faces two types of consumers. The inverse demand function of each type-1 consumer is P! = 100 − 2Q, while the inverse demand function of each type-2 consumer is:!P = 80 − Q. The firm’s cost function is given by: !C(Q) = 200 + 10Q. Suppose first that the firm is able to tell whether a consumer is of type-1 or type-2 (e.g. by checking some form of ID). Suppose also that the firm...
A monopolist faces the demand function Q = 20 – 2P. Its cost function is TC(Q)...
A monopolist faces the demand function Q = 20 – 2P. Its cost function is TC(Q) =0.5Q. Solve for the monopolist’s profit-maximizing price and output and calculate its profit as well as the consumer surplus and deadweight loss.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT