3. Two firms produce homogeneous products and each firm can produce a quantity be- tween 0 and 1000. There are 1000 potential buyers. Each of these buyers demands one unit of the firms' output, and has a reservation price of reservation price of $200 (that is, they buy one unit if and only if the price is $200 or lower). So both firms have enough capacity to supply the entire market. These two firms simultaneously choose prices and buyers buy at the cheaper price (if the price is $200 or lower). If the prices are the same, buyers choose a firm with equal probability. (a) Suppose both firms' unit cost of production is $100. Assume the price can only be in whole dollar amount. Explain that both charging $101 is a Nash equilibrium. (10 pts) (b) Suppose both firms' unit cost of production is $100. Assume the price can be any positive real number. Explain that both firms charging a price of $100 is a Nash equilibrium (10 pts) and that there is no other pure-strategy Nash equilibrium (10 pts)