Problem 3. Bob's risk preference is represented by the following expected utility formula: U (π, C₁; 1-T, C₂) = π r log(c₁) + (1 − π) log(C₂).
Bob can invest $10 into two stocks. Stock 1 returns $1 when the economy is good and returns 0 when the economy is bad while Stock 2 returns $0 when the economy is good and returns $1 when the economy is bad. The price of stock p₁ is denoted by p₁ and the price of stock 2 is p₂ = 0.25. Suppose the economy is good with probability 0.7 and is bad with probability 0.3. i) Write down Bob's utility maximization problem. ii) Determine Bob's optimal investment bundle (c₁, c) as a function of p₁. Draw the inverse demand curve for stock 1 (i.e., con X axis and p₁ on Y axis).