A risk-neutral firm is considering expanding output to supply an expected increase in demand. The cost of this initiative is expected to be $2 million (probability 0.8) or $3 million (probability 0.2). Revenues will be $5 million if demand is indeed strong (probability 0.7) but only $3 million if demand is weak (probability 0.3). Construct a decision tree to determine whether the firm should undertake the expansion. Then respond to the following items. 1. Explain why a bad outcome can occur from a good decision. 2. Can a firm benefit from a transaction that produces a negative expected return? Explain. 3. Explain risk aversion and risk neutrality, and apply those concepts to this case. 4. State lotteries have a negative expected payout to buyers of tickets. (Much of the proceeds are used to fund education and other programs run by the state). However, many people buy lottery tickets on a regular basis. a. Is this behavior rational? Explain. b. Some surveys of state lottery ticket buyers indicate that people are happy to buy a ticket for $1 with a possible prize of $5,000. Fewer, however, would buy a ticket for $100, with a possible prize of $500,000. The ratio of possible prize to ticket cost is the same. Why is the second ticket much less popular? Your total response (decision tree and answers to the questions) should be a minimum of two pages in length, and both parts should be uploaded as one document. You must use at least one academic source in your answer. Any information from outside sources must be cited in APA format.