Question 3 In this question you will examine the role of the price taking assumption in Walrasian equilibria. This will be done by comparing outcomes when firms choose prices in a Nash equilibrium and when firms simply respond to prices as in a Walrasian equilibrium. Bunters utility for a quantity x1 of product 1 and quantity x2 of product 2 is given by the utility function U (x1, x2) = 0.6 ln(x1 + 1) + 0.4 ln(x2 + 1). Product 1 is sold by firm 1 at unit price p1 and product 2 is sold by firm 2 at unit price p2. Bunter has an income of $100. Production costs for each of the firms is US$ 2 per unit. 1. What are Bunters utility maximizing demands for products 1 and 2 as a function of p1 and p2? 2. Suppose the firms simultaneously choose their prices. Given those prices, Bunter chooses a utility maximizing bundle. What price will each firm choose in a Nash equilibrium? 3. Suppose pi > 2 and firm i can sell any amount at this price. What is the profit maximizing supply of good i that firm i will supply? 4. Suppose pi < 2 and firm i can sell any amount at this price. What are the profit maximizing quantities of good i that firm i will supply? 5. Suppose pi = 2 and firm i can sell any amount at this price. What are the profit maximizing quantities of good i that firm i will supply? 6. What are the Walrasian equilibrium prices for goods 1 and 2.