Consider a beach in the south of Portugal that has length of 4. Two local citizens...

 

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Consider a beach in the south of Portugal that has length of 4. Two local citizens have specialized in selling seashells that they collect during the whole month in order to sell them on the first Sunday of each month (the busiest day at the beach). On that day each seller sets up its business at some specific point along the beach. During that day there will be 100 consumers, uniformly distributed along this beach, willing to buy seashells from these entrepreneurs. As the beach sand is very hot, the consumers incur into a transportation cost of 3(x-v)2, measured in euros, if they visit a seashell seller, where x is the location of the customer and v is the location of the seller. Each consumer always buys one seashell as long as the sum of the price paid and the transportation cost does not exceed their reservation price of 50€. Assume that marginal costs are zero for both sellers. a) Explain what market outcome would arise if both sellers were to locate in the centre of the beach. b) If each seller locates in one of the extremes of the beach, both would set a price of 36 €. Compute the profits and check that all 100 consumers will want to buy seashells. c) One seller wants to locate in the beach centre on the next day, while he expects his rival to stay in one of the extremes. The seller changing the location expects that in the Nash equilibrium he will set a price of 28€, while his rival will set a price of 20€. Compute the profits of each seller and explain whether this move would be strategically correct, by referring to the relevant principle of differentiation. Both of the sellers were engaging in this activity as they were waiting for job offers in the banking industry. Those offers just arrived and each seashell seller knows also the salary that was offered to his rival. In order to accept the job offer they will need to stop the seashell business. d) Explain in detail to what extent this new information influences whether you consider the move in part c) as strategically correct. e) If there were only one seller in the market, what would be the profit-maximizing price, assuming he wishes to cover the entire market. Consider a beach in the south of Portugal that has length of 4. Two local citizens have specialized in selling seashells that they collect during the whole month in order to sell them on the first Sunday of each month (the busiest day at the beach). On that day each seller sets up its business at some specific point along the beach. During that day there will be 100 consumers, uniformly distributed along this beach, willing to buy seashells from these entrepreneurs. As the beach sand is very hot, the consumers incur into a transportation cost of 3(x-v)2, measured in euros, if they visit a seashell seller, where x is the location of the customer and v is the location of the seller. Each consumer always buys one seashell as long as the sum of the price paid and the transportation cost does not exceed their reservation price of 50€. Assume that marginal costs are zero for both sellers. a) Explain what market outcome would arise if both sellers were to locate in the centre of the beach. b) If each seller locates in one of the extremes of the beach, both would set a price of 36 €. Compute the profits and check that all 100 consumers will want to buy seashells. c) One seller wants to locate in the beach centre on the next day, while he expects his rival to stay in one of the extremes. The seller changing the location expects that in the Nash equilibrium he will set a price of 28€, while his rival will set a price of 20€. Compute the profits of each seller and explain whether this move would be strategically correct, by referring to the relevant principle of differentiation. Both of the sellers were engaging in this activity as they were waiting for job offers in the banking industry. Those offers just arrived and each seashell seller knows also the salary that was offered to his rival. In order to accept the job offer they will need to stop the seashell business. d) Explain in detail to what extent this new information influences whether you consider the move in part c) as strategically correct. e) If there were only one seller in the market, what would be the profit-maximizing price, assuming he wishes to cover the entire market.

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Explain what market outcome would arise if both sellers were to locate in the centre of the beach If both sellers were to locate in the centre of the beach they would split the market evenly and each ... View the full answer