Problem 1. An investor has $2 billion in capital and he is planning to launch a pharma- ceutical businesses that can be involved in drug manufacturing, drug development, or both. Each $1 billion invested in drug manufacturing will produce a return of $2 billion, resulting in a profit of $1 billion. It costs $1 billion to attempt to develop a drug. For each drug developed, with 90% probability, the drug development attempt is a complete failure, re- sulting in a profit of -$1 billion. With 10% probability, the drug development is a success that yields a return of $25 billion for a profit of $24 billion. The success of different drug development attempts are independent to each other. The three possible business plans are: [22 TOTAL POINTS]

1. Spend $2 billion on drug development to attempt to develop two drugs

2. Spend $1 billion on drug development to attempt to develop one drug and spend $1 billion on drug manufacturing

3. Spend $2 billion on drug manufacturing a. What is the optimal business plan for a risk-neutral investor? [3 points]

b. A different investor has the following utility function: U(x) = x if x 0 and U(x) = 2x if x < 0 where x denotes profits. Whats the optimal business plan for this investor? In other words, this investor is loss-averse. [7 points]

c. Another investor is not only loss-averse but also keeps profits and losses from man- ufacturing and development in separate mental accounts. His utility function is given by: U(xm,xd) = m(xm)+d(xd) where m(xm) = xm if xm 0 and m(xm) = 2xm if xm < 0 andwhered(xd)=xd ifxd 0andm(xd)=2xd ifxd <0. Inwords,m isprofitsfrom manufacturing while d is profits from development. Whats the optimal business plan for this investor? [7 points]

d. The equity premium puzzle is the observation that in a model that assumes no men- tal accounting and no kinks in the utility function over profits, the demand for risky stocks

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relative to safe bonds is surprisingly low. Could loss aversion and mental accounting explain the equity premium puzzle? (Hint: you need to rely on the results from part b) and c). [5 points]