Consider two firms that produce identical products and compete in prices (i.e. their strategies are their prices). The marginal cost of both firms is 0 and there is no fixed cost. The prices charged by firm 1 and firm 2 are denoted by p1 and p2, respectively.

The maximum quantity of the product each one firm can produce is 1/4.The demand function is given by q = 1 - p where q is the quantity demanded and p is the lower price of the two. If the demand for the product of the firm that charges the lower price is above 1/4, then the firm cannot serve the entire demand, so that the firm produces 1/4 and the demand for the product of the other firm is 3/4 - p',where p' is the price of the firm that charges the higher price. If p1 = p2, then the demand is shared equally between the two firms.

1,Discuss whether p1 = p2 = 0 is a Nash equilibrium. You may answer in words or by using mathematics. Hint: considerthe profit of each firm, and check whether they have incentive to increase their price from 0.

2.Discuss whether p1 = p2 = 1/2 is a Nash equilibrium.Your answer must involve rigorous mathematical reasoning.