Consider a market with two firms. Each firm is located at one end of a line with lenght one. There is a mass one of consumers. The location of each consumer is given by 0 < x < 1 which is uniformly distributed (with density 1). Firms have no cost of production and set price simultaneously. a) Derive the demand for each firm by identifying the location of the indifferent consumer for each price pair. Assume that all consumers know about both products. b) Write down the profit functions and calculate the Nash equilibrium prices for both firms. c) Assume that consumers only know the product if they have received and ad. Suppose that ads are not targeted and each firm reaches any consumer with probability 0.5 with her ad. Calculate the size of the different consumer segments. Determine the resulting demand and the new Nash equilibirum prices of the firms. d) Suppose that the ads are costless. When do the firms make larger profits? With fully informed consuemers b) or with imperfect ads c)?
Consider a market with two firms. Each firm is located at one end of a line with lenght one.
There is a mass one of consumers. The location of each consumer is given by 0 < x < 1 which is uniformly distributed (with density 1). Firms have no cost of production and set
a) Derive the demand for each firm by identifying the location of the indifferent consumer for each price pair. Assume that all consumers know about both products.
b) Write down the profit functions and calculate the Nash
c) Assume that consumers only know the product if they have received and ad. Suppose that ads are not targeted and each firm reaches any consumer with probability 0.5 with her ad. Calculate the size of the different consumer segments. Determine the resulting demand and the new Nash equilibirum prices of the firms.
d) Suppose that the ads are costless. When do the firms make larger profits? With fully informed consuemers b) or with imperfect ads c)?
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