Suppose an oil company has discovered a new oil reserve. The company can construct either of large-capacity facility or a small-capacity facility (but not both or a mix of the two). The size of the facility the firm would want to construct depends on the amount of oil in the reservoir. To simplify, assume that there are two relevant sizes to the reservoir: large or small. If the firm builds a large facility and the reservoir is large, the firm's profit is $50 million. If the firm builds a large facility and the reservoir is small, profit is $10 million. If the firm builds a small facility and the reservoir is small, profit is $20 million. If the firm builds a small facility and the reservoir is large, profit is $30 million. But the oil company does not know the size of the reservoir. It believes that the reservoir will be large with probability 0.40 and small with probability 0.60. Assume the firm's preference is expressed by U (W)=(w^1-r )/(1-r), where W is the realized profit and r > 1 is the risk-aversion parameter.

• What is the optimal ex-ante investment decision, for a range of values for 1 < r < 100? Remember that the decision is a one-time binary one, meaning that the oil company should decide in advance to either build a large or a small facility. You should find the optimal size (small or larger) as a function of r