2. Imagine that a large number of consumers are uniformly distributed along a boardwalk that is 1 mile long. Hint: "Unif

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2 Imagine That A Large Number Of Consumers Are Uniformly Distributed Along A Boardwalk That Is 1 Mile Long Hint Unif 1 (113.6 KiB) Viewed 13 times

2. Imagine that a large number of consumers are uniformly distributed along a boardwalk that is 1 mile long. Hint: "Uniformly distributed" is a mathematical expression which refers to the uniform distribution of a continuous random variable. In this exercise, it essentially describes a situation such that • half of the consumers are located along the first half mile of the boardwalk, and the other half of the consumers are located along the second half of the boardwalk; and • in general, x% of the consumers are located along the first x/100 miles of the board- walk, where a can take any value between 0 and 100. Ice-cream prices are regulated, so consumers go to the nearest vendor because they dislike walking (assume that at the regulated prices all consumers will purchase an ice cream even if they have to walk a full mile). If more than one vendor is at the same location, the vendors split the business evenly. • Consider a game in which two ice-cream vendors pick their location simultaneously. Show that there exists a unique pure-strategy Nash equilibrium and that it involves both vendors locating at the midpoint of the boardwalk. 2 points