Even though they're separated, Paul and Camille decide to study a price-fixing agreement that will mutually benefit them. The idea is that they both agree to a price higher than the Bertrand equilibrium price, using the Grim Trigger strategy (if they detect a deviation from the agreed-upon price, they switch to playing the static Bertrand prices forever). What is the weakest assumption on the discount factor & e (0, 1) that supports the existence of a SPNE with collusion in this market (that is, a SPNE with a price strictly higher than the Bertrand equilibrium price from the previous question)?

Prospect X = ($4, 0.04 ; $15, 0.05 ; $24, 0.01 ; $38, p) What is the expected value of prospect X? (Hint 1: To answer this question, you'll need to first determine the value of "p"). (Hint 2: To determine "p", remember that probabilities sum to 1). (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)

Suppose you have a house worth $200,000 (wealth). Your utility of wealth is given by U(w) = ln(w). There is a small chance that a fire will damage your house causing a loss of $75,000. You estimate there is a 2% chance of fire. a) What is your expected wealth? b) What is your expected utility from owning the house? c) Suppose you can add a fire detection/prevention system to your house. This would reduce the chance of a bad event to 0 but it would cost you $C to install. What is the most you are willing to pay for the security system? (Here is an identity you will find useful

Billy John Pigskin of Mule Shoe, Texas, has a von Neumann-Morgenstern utility function of the form u(c) = √c. Billy John also weighs about 300 pounds and can outrun jackrabbits and pizza delivery trucks. Billy John is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,000,000 contract for playing professional football. If an injury ends his football career, he will receive a $10,000 contract as a refuse removal facilitator in his home town. There is a 10% chance that Billy John will be injured badly enough to end his career. If Billy John pays $p for an insurance policy that would give him $1,000,000 if he suffered a career-ending injury while in college, then he would be sure to have an income of $1,000,000 − p no matter what happened to him. Write an equation that can be solved to find the largest price that Billy John would be willing to pay for such an insurance policy. Here is my question: Why is Billy's income 1,000,000 - p even…