Solution_PS6_BEPP 250_S16

under his property. With 50% chance, the land only conserves limited amount of natural gas, in which case, he can drill and sell for 2 years. With 50% chance, the amount of natural gas is good for 10 years. The revenue of selling natural gas is $2,000,000 per year. There is a fixed cost of $1,000,000 per year for labor. If Jim shuts down the business, he doesn’t need to pay the labor cost. In the first year, Jim needs to purchase drilling equipment that would cost him an additional $5,000,000. The following table summarizes the information. Year 1 Year 2 Year 3-10 Cost Revenue Cost Revenue Cost Revenue Low amount $6M $2M $1M $2M $1M 0 High amount $2M $2M $2M Assume Jim is risk-neutral and his discount factor is 1. a. Would Jim invest in the business of drilling and selling natural gas? Answer: Suppose Jim invests. If the land conserves high amount of natural gas, Jim’s revenue is $ 2 M ∗ 10 = $ 20 M and the cost is $ 1 M ∗ 10 + $ 5 M = $ 15 M . Then Jim’s profit is $ 20 M − $ 15 M = $ 5 M . If the land conserves low amount of natural gas, Jim has the option to shut down the business starting from Year 3. His revenue is $ 2 M ∗ 2 = $ 4 M and his cost is $ 1 M ∗ 2 + $ 5 M = $ 7 M . Then Jim’s net profit is - $ 3 M . Since there is 50% chance of high amount and 50% chance of low amount, Jim’s expected profit is 0.5 ∗ $ 5 M + 0.5 ∗ ( − $ 3 M ) = $ 1 M . Jim’s profit is positive if he invested in the first place. Thus, Jim would invest in the business of drilling and selling natural gas. Note that if Jim didn’t have the option to shut down if he learnt that the land conserves only low amount, he would have lost $ 4 M − $ 15 M =− $ 11 M . In this case, investing in the first place would not be appealing as the expected profit is negative. For part (b)-(c), suppose the union requires that the labor contracts must last at least 5 years. In other words, if Jim hires workers for the project in the first year, he needs to pay the labor cost of $1,000,000 for at least 5 years. To be clear, in the event that his land conserves low amount of natural gas, Jim can only drill and sell for 2 years, but he still needs to pay the labor cost for Years 3-5.

Answer: Since Geiko’s insurance can only attract high risk customers, there is a 3% chance that a car will be totaled. Geiko’s profit is $ 1,000 − 0.03 ∗ 30,000 = $ 100 e. Find the price P that maximizes Geiko’s expected profit. Answer: If P≤ 335.91 , then both customers would buy the insurance. Geiko’s profit is 2 P − ( 0.01 + 0.03 ) ∗ 30000 = 2 P − 1200 ≤ − 528.18 < 0. If 335.91 < P≤ 1005.5 , then only high risk customer would buy the insurance. Geiko’s profit is P − 0.03 ∗ 30000 = P − 900. If 1005.5 < P , no one would buy and Geiko’s profit is 0. Therefore, Geiko would set P = 1005.5 to maximize expected profit.