For this multipart question, you will write answers on a separate sheet of paper and upload your work in the appropriate portal for this question.Your work must beneat and clearand you mustshow all your steps and calculationsin deriving your answers.

Suppose that there are 100 consumers whose preferences for queen size mattresses are uniformly distributed over a unit interval characterizing the softness of the mattress.The leftmost end of the interval can be called Sinkingly Soft while the rightmost end can be called Rest on a Rock.Currently, there are two mattress producers in the market;Firm A is located at the leftmost endpoint, while Firm B is located at the rightmost endpoint.The marginal and average costs to the firms are constant and equal to $100.Consumers face a transportation cost of $50, where represents the distance between their most preferred mattress and the type they actually purchase.

a.Suppose Firm A charges $200 for a mattress and Firm B charges $230 for a mattress.How many mattresses will Firm A sell?Firm B?Compute each firm's respective profits.

b.Carefully graph the situation in part a;that is, graph the spatial market, the firms' locations, the delivered pricing schedules and indicate: i) the location of the marginal consumer, and ii) the market share for Firm A and the market share for Firm B.

c.The pricing in part a is not an equilibrium.What is the equilibrium price in this market?

d.Would the equilibrium price be different if instead, both firms were located in the middle of the interval?If so, what would the equilibrium price be?Explain your answer.