Exam 4: Uncertainty

Suppose a risk-neutral power plant needs 10,000 tons of coal for its operations next month.It is uncertain about the future price of coal.Today it sells for $60 a ton but next month it could be $50 or $70 (with equal probability).How much would the power plant be willing to pay today for an option to buy a ton of coal next month at today's price? (Ignore discounting over the short period of a month.)

A gamble can be described as "fair" if the expected value of the gamble (including any costs of play)is

Suppose a lottery ticket costs $1 and the probability that a holder will win nothing is 90%.What must the jackpot be for this to be a fair bet?

Suppose a lottery ticket costs $1and has a jackpot of $1,000.What must the probability of winning nothing be if the bet is fair?

Suppose a lottery ticket costs $1and has a jackpot of $1 million.What must the probability of winning nothing be if the bet is fair?

Continuing with the power plant from the previous question,suppose instead the price of coal next month could be $54 or $66 (with equal probability).Now how much would it be willing to pay for an option to buy a ton of coal oil next month at today's price?

Continue with the power plant from the previous question, where again coal currently sells for $60 a ton but will sell for either $54 or $66 next month with equal probability. Now suppose coal can be stored for a month at the cost of $2 per ton. How would the new alternative of being able to buy coal at today’s prices and store it affect the amount the power plant would be willing to pay for an option to buy coal next month at today’s prices?

Continuing with the same vacation-insurance company from the preceding question,what vacation-day price(s)would be acceptable to both the family and the insurance company?

If a fair gamble is played many times,the combined monetary losses or gains will