Suppose the hotel in the lecture example raised its price from $30 to $30.50. With the new price, the hotel expects 96 guests to arrive 5% of the time, 97 guests 10% of the time, 98 guests 20% of the time, 99 guests 30% of the time, 100 guests 25% of the time and 101 guests 10% of the time.
Calculate the expected revenue, expected variable costs and expected costs from overbooking. Using marginal analysis, should the hotel raise its price? Explain your answer.