Answer all questions. 

3) The total cost function of a toy factory is given by TC(Q) = 100 + 20Q + Q 2 . The market price in this competitive industry is Rs. 60. All firms are identical and face similar costs. [15] a) What is the profit maximizing price and quantity produced by this toy factory? [4] b) Is this industry in the long-run or short-run. Give justification. [2] c) What will be the market price in the long-run? [5] d) If the industry demand function is given by P(Q) = 8040 ? 2Q, what is the number of firms that operate in this market in the long-run

In the month of September, all of the walmart grocery stores in Virginia sold 429,382 eggs. In that same month, all of the walmart grocery stores in Texas sold 283,054 eggs. How many eggs did the Virginia and Texas walmart grocery stores sell all together in the month of September? Use 2 strategies to show how you found out how many eggs Walmart sold in September. Explain how you solved for the sum using words, diagrams, or equations.?

Gen. Robert E. Lee's Boyhood Home is for Sale The historic Virginia home that Confederate Gen. Robert E. Lee grew up in hit the market in April 2018 for $8.5 million. (Trapasso, C.)

Robert E. Lee's father Henry rented the home in 1812, according to The Washington Post. The family lived there for over 80 years, including Robert E. Lee from age five to when he went to West Point in 1825. He again visited five years after the Civil War ended, The Post reported. (Leayman, E.)

The home's other claim to fame is that President George Washington also dined and lodged there before the Lee family moved in. (Trapasso, C.) Built in 1795, the brick house was listed on the National Register of Historic Places in 1986. (Trapasso, C.) The home had been used as a residence until 1966. The Stonewall Jackson Memorial Foundation purchased the home and opened it to the public.

Unable to make ends meet, the foundation sold the home in 2000 to Mark and Ann Kington for $2.5 million. (Trapasso, C.)

The childhood home of Robert E. Lee that was listed in April 2018 for $8.5 million dollars, was sold in July 2020.

Public records show it sold for almost half the original asking price at $4.7 million. (Alexandria Living Magazine.)

In your initial response to the topic you have to answer all questions. You are expected to make your own contribution in a main topic as well as respond with value added comments to at least two of your classmates as well as to your instructor.

1. Calculate the annual compound growth rate of the house price since the house was sold to Mark and Ann Kington (since 2000) until the house was sold in July 2020. (The growth rate should be calculated to two decimals in percentage form. Round the number of years to the whole number). Please show your work

1b. House price when it was sold to Mark and Ann Kington (2000) - $2,500,000 3. House price when it was listed for sale in 2018 - $8,500,000 4. = 7.0352% 5. 2. Assume that the growth rate you calculated in question #1 prevailed since Robert E. Lee's father Henry rented the home in 1812. Calculate the price of the house in 1812. (Round the number of years to the whole number). (TIP: To get the answer correctly you need to use the price of the house in your calculations in dollars with all zeros). Please show your work.

1c. You were using the time value of money concept to answer question #2. Think about the time line for that problem. What is the time point 0 in that problem? Please explain your answer.

1d. Assume the growth rate that you calculated in #1 prevailed since 1795. Calculate the price of the house in 1795. (TIP: To get the answer correctly you need to use the price of the house in your calculations in dollars with all zeros). Please show your work.

1e. Assume that the growth rate you calculated in question #1 remains the same until the Stonewall Jackson Memorial Foundation purchased the home in 1966 and opened it to the public. Calculate the price of the house in 1966. (TIP: To get the answer correctly you need to use the price of the house in your calculations in dollars with all zeros). Please show your work.

1f. In 2018, the listed price of the house was $8.5 million. In July 2020 the house was sold to $4.7 million. Calculate the compound rate of this reduction in price

. Please explain your answer.

. Decision Making under Uncertainty I (14 points) A rm is being sued for patent infringement. The rm could settle the case for $500,000, or it could ght the case in court. The rm believm that if it takes the case to trial, it has a 50% chance of winning. If it wins the case, its overall cost will be $100,000 (legal fees). If the rm loses the trial, it will immediately appeal. The rm believes that the appeal will be granted with probability ,0. If the appeal is granted, the rm's overall cost will be $150,000. If the appeal is dismissed, then the rm expects the overall cost (the sum of award against the rm, rm's own cost, winner's costs, etc.) to be $2 million. (a) (3 points) Draw a decision tree illustrating all strategies and payoffs (i.e., costs) for the rm. (b) (2 points) What is the expected payoff from appealing? (c) (3 points) What is the expected payoff from ghting the case in court? (d) (2 points) Should the rm settle the case ifp = 0.3? (e) (4 points) For what values of p should the rm settle the case? . Decision Making under Uncortainty II (21 points) Your utility U depends upon your income I as follows: U = VT. Your friend owes you $144. She offers you to roll a pair of dice. If you agree to play and roll a 2 or 4 (i.e., the sum of points on both dice is either 2 or 4), she will give you $324. If you roll anything but a 2 or 4, she will give you $81. If you refuse to play, you receive your $144 back. (a) (3 points) What is the probability of receiving $324? What is the probability of receiving $81? (b) (2 points) What is the expected payoff from playing the game? (c) (5 points) What is the expected utility from playing the game? (d) (5 points) Should you test your luck or refuse to play? Why? (e) (6 points) What is the minimum payment your friend should offer you in the event you win (i.e., roll a 2 or 4) to convince you to play? Collecting further information from the insured takes an average of 5 days to complete, and immediate settlement takes an average of 2 days before the settlement process is complete (state C). It is suggested that a time-homogeneous Markov process with states A, L, I, S and C could be used to model the progress of claims through the settlement system with the ultimate aim of reducing the average time to settle a claim. (i) Calculate the generator matrix, (1;;i, j = 4, L, I, S, C}, of such a model. [ (ii) Calculate the proportion of claims that eventually require more details from the insured. [2] (iii) Using a forward differential equation, derive an expression for the probability that a claim is yet to be logged and classified by a claims administrator at time . [4] (iv) Write down the backward integral equation for the transition probability Pay (t), and hence show that: PAr (t) = 0.05 ["e-0.50w PLI (t- w)dw +0.25e-0.201 [' e-0.30w [3] (v) Using the expression in (iv), show that: PAI (1) =- 3 -0.101 47 -0.20r 197 -0.50r 60 [6] 80 240 (vi) Calculate the probability that a claim is still awaiting information from the insured after 10 days. [1] (vii) Describe briefly how you could verify that this time homogeneous rather than an alternative time inhomogeneous model was a suitable model of the claims' settlement process. [2] [Total 20]