9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC - 100, +00, +10Q, where and 2 denote the quantity of items of goods 1 and 2, respectively that are produced. If P, and P, denote the corresponding prices then the demand equations are P = 50 –Q + Q. P, = 30 + 20, -Q. Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.

9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC - 100, +00, +10Q, where and 2 denote the quantity of items of goods 1 and 2, respectively that are produced. If P, and P, denote the corresponding prices then the demand equations are P = 50 –Q + Q. P, = 30 + 20, -Q. Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter14: Monopoly

Section: Chapter Questions

Problem 14.4P: Suppose the market for Hula Hoops is monopolized by a single firm. a. Draw the initial equilibrium...

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Question 10A monopolistic producer of two goods, G1 and G2, has a joint total cost function TC = 5Q1 + Q1Q2 + 5Q2Where Q1 and Q2 denote the quantities of G1 and G2 respectivel. If P1 and P2 denote the corresponding prices then the demand equations areP1 = 40 − Q1 + Q2P2 = 20 + 2Q1 − Q2a) Find the total revenue function for each goodb) Find the profit function for the firmc) Find the maximum profit if the firm is contracted to produce a total of 12 goods of either typed) Find the price that the firm is supposed to charge for each good.e) Estimate the new optimal profit if the production quota increases by 2 units
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1. A monopolistic producer of two goods, G1 and G2, has a total cost function TC = 5Q1 + 10Q2 where Q1 and Q2 denote the quantities of G1 and G2 respectively. If P1 and P2 denote the corresponding prices then the demand equations are P1 = 50 − Q1 − Q2 P2 = 100 − Q1 − 4Q2Find the maximum profit if the firm’s total costs are fixed at Gh100. Estimate the new optimal profit if total costs rise to Gh101.
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1.Amalgamated Popcorn, Inc. sells bags of flavored gourmet popcorn in a popular mall. As shop owner and operator, you have observed that weekly popcorn sales are well-described by the demand equation: Q = 1,200 -800P + 2.0A, where A denotes advertising weekly spending (in dollars). You are currently charging $1.50 per bag of popcorn (for which the marginal cost is $.75) and spending $500 per week on advertising. a) Compute the store’s price elasticity and advertising elasticity. b) Check whether your current $1.50 price is profit maximizing. If not, determine the store’s optimal quantity and price. c) Should the store consider increasing its advertising spending? Why or why not.
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Suppose you are employed at a monopolistic company as a research (pricing)economist and you are deriving the behavior of two markets based on demand curves given by: D1 (p1) = 50 - p1 D2 (p2) = 50 - 2p2 Assume that the marginal cost is constant at $8 a unit. (a) If it can price discriminate, what price should it charge in each market in order to maximize profits? (b) If it can't price discriminate, what price should it charge?