Suppose the government decides to set the price of the good equal to marginal cost and subsidize the firm in order to get the firm to produce enough output to satisfy the market at that price

home / study / business / economics / questions and answers / 1. (18 total points) suppose there are Show more home / study / business / economics / questions and answers / 1. (18 total points) suppose there are 8 firms Question 1. (18 total points) Suppose there are 8 firms located equidistantly around a circle whose circumference is equal to 1. There are 400 consumers distributed uniformly around the circle. Each consumer gets utility U = 3.5 from buying a unit of the good from a firm which sells their ideal brand (a firm located at the consumers location). Also the consumers utility decreases by 4 times the distance that the consumer is located from the firm. So a consumer who buys from firm i gets utility given by Ui = 3.5 4xi where xi is the distance from the consumers location to firm is location. The consumers surplus from purchasing a unit of the good from firm i is the difference between their utility from purchasing a unit of the good from firm i and the price that firm i charges. So CS = Ui Pi. Also the consumer has no alternatives so the consumer will buy a unit of the good if maximum surplus gained from purchasing from any firm is greater than 0. a) (6 points) Consider a particular firm denoted Firm 2. Let Firm 1 be the firm located on one side of Firm 2 and let Firm 3 be the firm located on the other side of Firm 2. Suppose Firm 1 charges a price P1 = 2 and Firm 3 charges a price P3 = 2. Write a general expression for Firm 2s demand. b) (4 points) Suppose Firm 2 can produce its good at constant marginal cost MC = 1.5. What price should firm 2 charge if it wants to maximize its profit? c) (4 points) Suppose the firm has no close neighbors so that it acts as a monopolist. Therefore it captures all of the consumers whose surplus is greater than or equal to 0. Write a general expression for the firms demand. d) (4 points) Suppose the monopoly firm can produce its good at constant marginal cost MC = 1.5. What price should it charge if it wants to maximize its profit? 2. (15 total points) Suppose that assuming a firm decides to produce a product it must build a production facility. The fixed cost of this facility is F = 90. Also the firm has constant marginal cost MC = 5. Demand for the product that the firm produces is given by P = 40-5Q. a) (8 points) On a single graph carefully draw the MC curve the demand curve and the ATC curve. Your graph should go up to 8 units of output. Please label your graph carefully. b) (3 points) How much output will this firm produce? Suppose the government decides to set the price of the good equal to marginal cost and subsidize the firm in order to get the firm to produce enough output to satisfy the market at that price. c) (2 points) How much should the subsidy be in order to allow the firm to make exactly zero profit. d) (2 points) How much consumer surplus will consumers get if P = MC? 3. (17 total points) Suppose there are two types of consumers: Type A and Type B. The demands for a monopolists product for each type of consumers are given by: Type A: Q = 90 2P Type B: Q = 60 4P Assume the marginal cost of production is constant and MC = 4 and there are no fixed costs. a) (5 points) Suppose the firm is unable to distinguish between the two types of consumers and therefore cannot engage in price discrimination. Sketch the demand curve facing the firm. Make sure your graph is accurate and carefully labeled. b) (2 points) What price will the monopolist charge? c) (2 points) How much profit will the monopolist make? d) (2 points) If the monopolist is able to charge different prices to each type of consumer what price will she charge to type A consumers? e) (2 points) What is the Price Elasticity of Demand for Type A consumers? f) (2 points) If the monopolist is able to charge different prices to each type of consumer what price will she charge to type B consumers? g) (2 points) What is the Price Elasticity of Demand for Type B consumers? Show less


 

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