5.(15 pts.) Fulbright and Smile are two toothpaste brands. In this duopoly, the market demand is given by the inverse demand function = 10 .005, where P is the price in dollars, and Q is the outpumeasured in thousands. Fulbright and Smile products are viewed very similar by the consumers such that the consumers will always buy the product with a lower price between the two. If the products are equally priced, consumers will always purchase Fulbright's products. Both companies' marginal costs are $5, and the pricing can only be done in exact dollars.

a)What are the strategy sets (, ) for Fulbright and Smile? (4 pts.

b)Find all nash equilibria. Make sure to justify your answer thoroughly. (6 pts.)

c)Prove that there are no other nash equilibria other than the nash equilibria from part b) Make sure to justify your answer thoroughly. (5 pts.)