# ECON 342 ECON342 Homework 3 with Answers (Penn State University)

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ECON 342 ECON342 Homework 3 Answer (Penn State University)

1.  (18 total points) Suppose there are 5 firms located equidistantly around a circle whose circumference is equal to 1.  There are 100 consumers distributed uniformly around the circle.  Each consumer gets utility U = 6 from buying a unit of the good from a firm which sells their ideal brand (a firm located at the consumer’s location).  Also, the consumer’s utility decreases by 5 times the distance that the consumer is located from the firm.  So a consumer who buys from firm i gets utility given by Ui = 6 – 5xi where xi is the distance from the consumer’s location to firm i’s location.  The consumer’s 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.

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.

Assume the marginal cost of production is constant and MC = 4, and there are no fixed costs.

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