Question 1: Consider a risk averse agent with utility function u(w) = w\

Question 1: Consider a risk averse agent with utility function u(w) = wa, a e (0, 1), where w 2 0 represents wealth. The agent faces the following gamble: With probability 1 p he gets $0, and with probability p he gets $1, where p e (0, 1). 1.1 What is the expected (monetary) value of the gamble? Formulate the expected utility and derive the certainty equivalent. Is the certainty equivalent increasing or decreasing in p? Is the consumer better off when p increases? 1.2 Prove that the conclusion you obtained in 1.1 holds for any utility function, u(w), with the properties that u(0) = 0, u' (w) > 0, u" (w) < 0 [you may use figures or math]. Carefully explain the intuition.