Which of the following expressions is the Lagrangian? O A. MUX=1PX В. бф = MUx(X,Y}- ¿Px %3D SX С. бф SA = PxX+P,Y-1 O D. 4 = U(X,Y) –-2 (PxX+P,Y-I)
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- It is known that the ABC oil company supplies consumers with 150 tons of products per day. The company produces only two types of products - gasoline and diesel fuel. The limiting transformation ratio of diesel fuel relative to gasoline is 0.5. a) Draw a line of the company's monthly production capacity for gasoline and diesel. b) With the advent of new technologies, production increased by 20%, and the availability of gasoline increased by 30%. Explain how the company's new product line differs from the previous one. c) If we put the gasoline production on the X-axis of the graph, what percentage of the slope capacity of the production line is different from the slope ratio of the previous production line?As a manager of a small software retailing company, you are concerned with projected profit next year. While profit can be determined as the difference between sales and maintenance cost, or in symbols, P = S - M, where P is profit, S is sales, and M is maintenance cost including technical support. It is argues that when sales goes up so does maintenance cost because the cost of technical support will go up. Further, it is measured that the correlation between S and M is 0.8. Now given the figure that sales next year is expected to be $300 thousand with standard deviation of $4 thousand and maintenance cost is expected to be $150 thousand with standard deviation of $6 thousand, what would be the expected profit and its standard deviation you will include in your report?In the past four years, the annual returns of one company’s stockare 12%, 18%, and –14%, and 7%.a) What is the geometric average return? b) What is the arithmetic average of the returns? c) According to an economist’ forecast on the Year 2020, the probabilities of repeatingthe performances of the former four years are 30%, 30%, 20%, and 20%, respectively.What is the expected return of the stock in the Year 2020
- 5. Consider the process where S0 = 0 and {ut : t ∈ Z} is an i.i.d. random variable with N(0,σ2). a) DeterminethemeanandcovariancefunctionoftheprocessSt.Isthisprocessstrictlystationary?Second-order stationary? b) Show that the process Yt = (1 − L)St , t = 1,2,... is strictly stationary. Compute its mean and autocovariance function.I cannot figure out how the equation goes from q1 = D1 (p1; p2) = S(1/2 + (p2-p1/2t)) to q1 = S/2 +(p2-p1/2t) why is S not in the numerator of both terms? i.e. q1 = S/2 + S(p2-p1/2t)Suppose that Var(X) = 661.1, Var(X) = 8021.53, and Cov(X,Y) = 1922.11. What is Var(.64X + .36Y)? Suppose that Var(X) = 869.03, Var(X) = 7850.84, and Cov(X,Y) = 2238.69. What is Var(.67X + .33Y)?
- Suppose the relationship between Y and X is given by: Y = 3.1415 + 6X + error By how much does the expected value of Y change if X increases by 7.23 units? (Round your answer to two decimal places: ex: 123.45)2. (+3) For events A, B, and C, state whether each of the following is always true (T) or not always true (F): (a) P(A|B) + P(A|B) = 1 (b) If A and B are independent events then A is independent of B. (c) If P(C) > 0 and P(A) > P(B) then P(A|C) > P(B|C).A farmer believes there is an equal chance that the next growing season will be abnormallyrainy. His expected return function has the formExpected return = 0.5lnYNR + 0.5lnYRwhere YNR and YR represent the farmer’s income in the states of “normal rain”and “rainy,” respectively.Suppose the farmer must choose between two crops that promise the following incomeprospects:Crop YNR YRMaize $14,000 $5,000Cotton $9,500 $7,500a) Which of the crops will he plant?b) Suppose the farmer can plant half his field with each crop. Would he choose to do so?Explain your result.c) What mix of Maize and Cotton would provide maximum expected utility to this farmer?d) Would Maize crop insurance, available to farmers who grow only Maize, which costs$2,000 and pays off $4,000 in the event of a rainy growing season, cause this farmer tochange what he plants?
- 2. Give an example of the time inconsistency problem applied to the relationship of a married couple.Q6 Suppose that at time t=0, half of a "logistic" population of 100000 persons have heard a certain rumor and that the number of those who have heard it is then increasing at the rate of 500 persons per day. How long will it take for this rumor to spread to 80% of the population? ( Suggestion: Find the value of k by substituting P(0) and P'(0) in the logistic equation) a. About 98 days b. About 34 days c. About 19 days d. About 69 days e. About 119 daysQ. 1 You are the mayor of a small town with 2000 residents. The head of your economic development agency recently conducted a survey in which the 2000 residents said that a public concert in the centre of town would be worth $20 to cach of them. Since it costs only $5000 to hold the concert, you organized and held the concert, which everyone in town enjoyed. But when you asked for donations to pay for the concert, you only collected $30 in total. What do you know? a. The survey certainly overstated how much the concert was worth to each resident. b. From the standpoint of total costs and benefits, the cost of the concert certainly exceceded the benefit. c. The concert was an example of the Tragedy of the Commons. d. Residents of the town were probably free riders.