The demand for yogurt in a county is dominated by two yogurt makers. One produces a non-fat yogurt, the other produces a full-fat yogurt. Consumer preferences are uniformly distributed along the line that goes from zero fat to the number unity that indexes full-fat. Each consumer buys a container of yogurt a week. A consumer that prefers zero fat feels a disutility of $2 if consumes a full-fat yogurt and conversely. Both firms can produce with a constant same unit cost $2 a. (5 pts.) Get the demands for each yogurt and find the reaction curves in the prices PNF and Pf . b. (5 pts.) Find the Nash equilibrium. Depict the reaction curves of both firms and the Nash equilibrium. What intuitively means that reaction curve of firm 1 is upward sloping? c. (5 pts) Following a heated discussion on the health and taste properties of non-fat and fat yogurts people do not change their preferences but feel much stronger about them. Now a consumer that prefers zero fat feels a disutility of $4 if consumes a full-fat yogur and conversely. Compute the new Nash equilibrium and show in a diagram the change in equilibrium. d. (5 pts.) The producer of full-fat yogurt decides to change to a low-fat yogurt that costs her the same and meets exactly the preference of the consumer at 0.5 If both producers keep the prices of part b explain with the help of a diagram what is going to happen with their market shares. e. (5pts.) Explain with the help of a new diagram what will happen if the non-fat producer moves also to produce a low-fat yogurt. What will be new Nash equilibrium? Do the producers prefer this or the equilibrium at part b?