There are N consumers uniformly distributed along a linear city of unit length, served by two shops located at opposite extremities of the city. The two shops sell an identical product, for which consumers have unit demands, and they have identical constant marginal costs of 2 and no fixed costs. The cost to consumers of travelling the length of the city is 4. a) Making clear your assumptions and calculations, work out the optimal prices the shops should charge for the product, and their profits in terms of N. How does your result relate to the so-called Bertrand Paradox? b) Explain why it is optimal for the shops to locate at opposite ends of the city. c) Suppose one shop only has a marginal cost of 1, but there are no other changes to the setting. Calculate the optimal prices for the shops, and their profits in terms of N.
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2. There are N consumers uniformly distributed along a linear city of unit length, served by two shops located at opposite extremities of the city. The two shops sell an identical product, for which consumers have unit demands, and they have identical constant marginal costs of 2 and no fixed costs. The cost to consumers of travelling the length of the city is 4.
a) Making clear your assumptions and calculations, work out the optimal
b) Explain why it is optimal for the shops to locate at opposite ends of the city.
c) Suppose one shop only has a marginal cost of 1, but there are no other changes to the setting. Calculate the optimal prices for the shops, and their profits in terms of N.
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