Following is a list of information for Michael and Diana Lapin for the tax year 2019. Michael and Diana are married. Michael is a lawyer working for a Native American law firm, Native American Justice, Inc. Diana works part-time for Creation, a genetic research lab. Paul Harris, he is 50 years old and a homeless family-friend that lived all year in the lapin’s basement. The Lapin’s provide all of Paul’s support. Assume that all other requirements are met by each potential dependent. Can the Lapin claim him as a dependent for tax purposes?

a) Write the payoff functions for the European and American up-and-in barrier put option with barrier B.

b) Use the 4-step binomial tree to price the up-and-in barrier put options (European style and American style, separately). Assume that the spot price is $105. The strike is $101. The barrier is $106. The time to maturity is 1 year. Risk-free rate is 5% with the annual compounding, the stock price goes up or down by 20%.

c) Is the European up-and-in barrier put option priced higher or lower than the same option wihout a barrier?

a. Donna donates stock in Chipper Corporation to the American Red Cross on September 10, 2018. She purchased the stock for $24,325 on December 28, 2017, and it had a fair market value of $34,750 when she made the donation.

The stock is treated as (capital gain or ordinary income) property and Donna's charitable contribution deduction is $ ______tax purposes.

b. Assume instead that the stock had a fair market value of $20,850 (rather than $34,750) when it was donated to the American Red Cross. Donna's charitable contribution deduction would be $_______ for tax purchases.

Suppose one Japanese firm and one American firm dominate the US market of widgets. They share the same cost structure: TC = 250 + 40q. The only demand for widgets is in the US and is p = 100 – Q.

(a) If these two firms compete in quantity at the same time, what is the Cournot equilibrium output, price, profit level by each firm?

(b) Suppose the American firm acquires the Japanese firm and therefore becomes a monopoly in this market. Calculate the monopoly’s output, price, and Lerner Index. How much is the deadweight loss due to monopoly behavior?

Ray Ray made the following contributions this year.

American Heart Association plans to sell the stock to fund its operations. First Methodist Church intends to sell the antique painting. Ray Ray has owned the painting and Coca-Cola stock since 1990.

What is the total amount of charitable contributions subject to the 30% of AGI ceiling?

1. Construct a Pie Chart:

You obtained the following data related to demographics in your statistics class:

Race                                                   Number of Students

Hispanic                                             15

Asian                                                  10

African American                             12

Caucasian                                          19

Native American                              5

What can you infer from your data?

2. Construct a Bar Graph:

You obtained the following data related to demographics in your statistics class:

Religion                                                            Number of Students

Christian                                                           17

Muslim                                                              18

Buddhist                                                           19

Catholics                                                          20

Not Religious                                                  24

What can you infer from your data?

1. What is the price of an American-style call option assuming a 4% annual risk-free rate, a strike price = $150, and 3 years to maturity.  In each year the price can either rise by a factor of 1.3 or fall by a factor of 0.9.  The current price of the underlying asset is $100 and it pays no dividends.
2. Why is the price in part a different than you would get from inputting a 10% drift and 20% volatility into the Black Scholes equation?
3. What would be the price of an American-style put option on the same stock with the same maturity as in part a above?

1. What is the price of an American-style call option assuming a 4% annual risk-free rate, a strike price = $150, and 3 years to maturity.  In each year the price can either rise by a factor of 1.3 or fall by a factor of 0.9.  The current price of the underlying asset is $100 and it pays no dividends.
2. Why is the price in part a different than you would get from inputting a 10% drift and 20% volatility into the Black Scholes equation?
3. What would be the price of an American-style put option on the same stock with the same maturity as in part a above?

Hardly a day goes by without some new poll being published. Polls influence the choice of candidates and the direction of their policies, especially during election campaigns. For example, the Gallup Organization polled 1012 American adults, asking them, ``Do you think there should or should not be a law that would ban the possession of handguns, except by the police and other authorized persons?'' Of 1012 randomly chosen respondents, 374 said that there should be such a law. Construct a 95% confidence interval for the population proportion of all American adults who think there should be such a law.

2. (8 pts.) The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among American women ages 20 to 24 is 2791.5 per 100,000. Take a random sample of three American women in this age group. (a) What is the probability that all of them have a Chlamydia infection? (b) What is the probability that none of them has a Chlamydia infection? (c) What is the probability that at least one of them has a Chlamydia infection? (d) What is the probability that at most one has a Chlamydia infection?

Please show work and explain.