competitive allocation.) (Hint: with one 2 products, you can safely set the price of y to 1, and then solve only for the price of x.) 2. (12 marks) Players play the following normal form game repeatedly, forever. They play the game once in each period. Assume that the interest rate is r. Show that it is possible to sustain the outcome {U, L} if r is sufficiently low. 3. (10 marks) Portia has waited a long time for her ship to come in, and she has concluded that it will arrive today with probability 0.2. Portia already has $49. If the ship does come, she will receive an additional $25. If it doesn't come in today, it never will and she will have $49. She has a von Neumann-Morgenstern utility function equal to the square root of her total income. What is the minimum price at which she would sell the rights to her ship? 4. (10 marks) Find all the sub game perfect Nash equilibria of the following game (if there are any). If there is no sub-game perfect Nash equilibrium, say so. Assume that player 1 moves rst, then player 2