Question 1 ( A monopolist sells Soma at the same price into two different markets. The inverse demand fo Soma in market #1 is denoted p1(q) = 15 – q. The demand for Soma in market #2 is given bị D2(p) = 80 – 3p. Assume the monopolist's cost function is C(q) = log(1 +q), where q represent the total quantity produced. (Note: (1) log denotes natural logarithm; (2) Round all answers to 2 decimal places. %3D 1. What is the profit maximizing quantity for the monopolist?

Question 1 ( A monopolist sells Soma at the same price into two different markets. The inverse demand fo Soma in market #1 is denoted p1(q) = 15 – q. The demand for Soma in market #2 is given bị D2(p) = 80 – 3p. Assume the monopolist's cost function is C(q) = log(1 +q), where q represent the total quantity produced. (Note: (1) log denotes natural logarithm; (2) Round all answers to 2 decimal places. %3D 1. What is the profit maximizing quantity for the monopolist?

Survey Of Economics

10th Edition

ISBN:9781337111522

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter8: Monopoly

Section: Chapter Questions

Problem 7SQP

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Question 1 A monopolist sells Soma at the same price into two different markets. The demand for Soma in market #1 is denoted D1(p) = 30 – 2p wherep is the unit price. The demand for Soma in market #2 is given by D½(p) = 80 – 3p. Assume the monopolist's cost function is C(q) = cq where represents the quantity produced. 5. If c = 1.5 compute the optimal price for the monopolist to charge using the markup formula.
Question 2. A monopolist sells the same product at the same price into two different markets. The demand for the product in market #1 is denoted D₁ (p) = 30 - 2p where p is the unit price. The demand for the product in market #2 is given by D₂ (p) = 80 - 3p. (a) If the monopolist sets a price of $20 per unit, what is the total demand? (b) Explain why elasticity of total demand is not defined at a unit price of $15.
Question 4. Consider a monopolist facing a demand curve of the form D(p) = 100 – 2p where p is the - unit price. Suppose the monopolist has a constant marginal cost of production of $2 a unit. Bunter was asked to determine the price which would maximize consumer surplus. Here is his solution: Total surplus as a function of price is 50(100 – 2x)dx. The derivative of this with respect to p is -(100-2p). This is maximized by making p as large as possible, i.e., p = 50. Is Bunter correct? If not, what is the error that Bunter has made?
2. Consider a monopolist who has a cost function of c(Q) = 5Q. This monopolist faces two consumers, the first having demand q₁(P₁) = 80 - 2P₁ and the second having demand q₂ (P₂) = 50 - P₂. 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 and 2 (they should be different), and calculate the monopolist's profits. How do they compare to the profits in part (a)?
All 20 consumers are alike and each has a demand curve for a monopolist's product of p=15 -3q. The cost of production C(Q) =2Q. Let the monopolist charge a price of $PM for qM unit purchased. Find the menu prices that maximize profits? (The buyer pays menu price PM for quantity qM) What is the maximum profit the monopolist can earn in this market? (pi)?
A monopolist's demand function is given by D(p) = 90 – 2p. This - monopolist is facing a cost function, C(y) = (1/2)y² + 600. (a) Is this a natural monopoly? Explain. (b) How can government regulate this monopolist to produce the efficient amount of products?
A monopolist supplies an identical good in both countries. The inverse demand curve of Country A is P = 12 – Q and that of Country B is P = 22 – 2Q. Suppose the monopolist has plants in two countries and all plants have a constant marginal cost of $2. (a) Suppose the tariff is so high that there is no trade between the two countries, what price should the monopolist charge in each country? What is its total profit? (b) After the two countries sign a trade agreement, the tariff becomes zero. Now the good the monopolist supplies can be transported from one country to the other with a cost of one dollar per unit. How will the monopolist’s profit change if it does NOT change its pricing strategy? (c) How should the monopolist change its pricing strategy to maximize its profit?
Q)(a) What is the monopolist’s marginal revenue at a production level? (b) What is the monopolist’s profit-maximizing output level? (c) What is the profit that the monopolist can earn in equilibrium?
Only part (c) please, thank you.
4) A monopolist faces a market inverse demand function: P = 250 – 5Q and marginal cost function: ATC = MC = 10. Answer the following. If the monopolist employs a single price strategy, what is the optimal quantity produced and price charged. What is the market up and contribution margin from the strategy in part a if Ed = -1.0833. If other firms trying to enter this market had slightly higher cost structures, what would be a good price & quantity mix to limit entry of competition and why (no math needed). If the monopolist could create a bundled good instead of the strategy in part a, what price would it charge and how many units would be sold in the bundle. What are the profits from part a & part d? Which pricing strategy is preferred. EC: Briefly explain why a firm that offers a buy 2 get the 3rd free deal, does not just offer that same product at a 33.33% discount of the normal stated price. I need help with number 4
A monopolist faces the following market demand function: D(P) = 100 – P and has total costs equal to TC(Q) = 100 + 100 Show that the monopolist's cost function is subadditive for all relevant levels of demand (for all Q< 100). (Hint: Let EN Qi = Q be a way to split up the total production of quantity Q in N different firms. You can then use the fact that the minimum of EN Q? is reached at Qi = 8.)
5) A monopolist sells its product to two countries, labeled 1 and 2. The inverse demand curves in these countries are p1 = 100 – Q, and p2 = 120 – 3Q2. respectively. The monopolist's cost function is C(Q) =02, where Q = Q1 + Q2- a) Find the aggregate demand function and the associated inverse demand function for p < 100. Write down the monopolist's profit function and proceed to find its profit-maximizing output and profit. Calculate the equilibrium price the monopolist would charge in each country. Also calculate the output it would supply to each country. b) c)