The local movie theater industry has a demand curve of P=26-.2Q for a movie showing (please note the decimal in front of the 2). It has a supply curve (MC curve) of $2, because the theater figures for each customer there will be a cleanup cost afterwards. In reality, a theater might sell food and drinks for extra profits, but this one does not.

1. What is allocative efficiency? What is the price of a ticket and number of patrons (quantity) that will result in allocative efficiency? Why is this price not practical?
2. If the theater, the only one in town, wishes to price as a monopoly, what would the price of a ticket and quantity (number of patrons) be?
3. If this theater would like to price discriminate by charging some $20 and letting them sit in the front rows, regular customers the monopoly price, and senior citizens who do not sit in the front $5, by how much would the $20 price increase profits over a regular monopoly price? By how much would the $5 price increase profits over the regular monopoly price? By having three prices instead of one, how much would profit increase by? Explain your answers and demonstrate with a graph.
4. Assume another theater opens so there are two theaters in town. The marginal cost and demand curve remain the same for the industry, but there are now two firms instead of one. Use the Cournot model of duopoly to determine the new movie theater ticket price with two theaters instead of one. Explain your answer and include a graph.
5. What would be the Lerner Index for these two theaters? What does this number measure?

In an old-fashioned amusement park ride, passengers stand inside a 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will "stick" to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.62 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says "No children under 30 kg allowed."

Q: What is the minimum angular speed, in rpm, for which the ride is safe?

In an old-fashioned amusement park ride, passengers stand inside a 4.5-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will "stick" to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.65 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says "No children under 30 kg allowed." What is the minimum angular speed, in rpm, for which the ride is safe?

James is a college senior who is majoring in Risk Management and Insurance. He owns a high-mileage 1998 Honda Civic that has a market value of $2,800. The current replacement value of his clothes, television sets, stereo set, cell phone, and other property in a rented apartment totals $9,000. He has a waterbed in his rented apartment that has leaked in the past. An avid runner, James runs 5 miles daily in a nearby public park that has the reputation of being very dangerous because of drug dealers, numerous assaults and muggings, and drive-by shootings. For each of the following risks or loss exposures, identify an appropriate risk management technique that could have been used to deal with the exposure. Explain your answer. (3 questions)

1. Liability lawsuit against James arising out of negligent operation of his car

2. Waterbed leak that causes property damage to the apartment

3. Physical assault on James by gang members who are dealing drugs in the park where he runs

An elementary reaction A+B  C+D is to be carried out in a non-ideal CSTR which has both bypassing and a stagnant region in this reactor. The measured reactor volume is 1.0 m3 and the flow rate to the reactor is 0.1 m3/min. The reaction rate constant is 0.28 m3/kmol.min. The feed is equimolar in A and B with an entering concentration of A equal to 2.0 kmol/m3 k. Calculate the conversion that can be expected in this reactor if the model parameters of α and β were determined from a tracer test and were found to be 0.8 and 0.3 respectively.

The monthly ambulatory visit shown in the Table below occurred in an outpatient clinic.

1. Prepare a forecast for January visits, using the simple exponential smoothing method with α = 0.3.
2. If α = 0.5, what is the predicted value for January visits?
3. If α = 0.0, what is the predicted value for January visits
4. If α = 1.0, what is the predicted value for January visits
5. Which alpha produces the best forecast?

You own a portfolio of two stocks. Red River Inc. has an expected return of 9% and a standard deviation of 15% while Boston Harbor Co. has an expected return of 15% with a standard deviation of 19%.

a. What percent of your portfolio must you invest in each stock if you wanted to earn a 12.4% return on the portfolio? (Hint: Consider W1+W2=1.0)

b. If the correlation coefficient is 0.3, what is the standard deviation of this portfolio? Is risk reduced at these weights relative to the risk of the individual assets? Why?

Use the above information from the tables to work out the following missing entries, and then calculate the company’s return on equity. Note: Turnover and the average collection period are calculated using start-of-year, not average, values. (Enter your answers in millions. Round intermediate calculations and final answers to 2 decimal places.)

Consider a portfolio dependent on the price of a single asset that is delta neutral, with a gamma of -6000 and a vega of -9600. Suppose that a traded option (called Option 1) with a delta of 0.3, a gamma of 0.5 and a vega of 1.0 is available.

1. How could the portfolio be made delta and gamma neutral?
2. How could the portfolio be made delta and vega neutral?
3. If another traded option (called Option 2) with a delta of 0.7, a gamma of 1.2 and a vega of 1.6 is available. How could the portfolio be made delta, gamma and vega neutral?

A movie theater is planning to offer the possibility to book the seats either online or at the kiosk of the theater. Design the booking application for the theater taking in account the following consideration:

- The theater has 100 seats only.

- More than one user may be trying to book the same seat at the same time.

- Any seat can be booked by only one user.

- A seat can be available for the kiosk agent and the online user at the same time but can be booked by only one of them.

- If the client did not book a seat online or changed his/her mind at the kiosk, the seat must be available again for booking.

Use the process synchronization techniques. You are allowed to use variables as much as you need in the design.

The code does not have to be complicated or detailed. Thanks for the help!