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Question 3 The following data relate to length of public roads (in '000 km) and number of goods vehicles with current licenses (in '000) for eight successive years:: Length 316 318 320 322 325 327 329 331 of roads Number 1692 1640 1640 1630 1632 1660 1736 1778 of licenses Required: Find the coefficient of linear correlation. Question 4 On ten different days (picked at random) the following values were obtained for the price of a share for a particular company together with the value of FTSE (Financial Times Stock Exchange) Index on that day: Share 77 46 80 76 65 71 60 75 76 88 Price (in pence) FTSE 319 315 387 339 383 340 340 356 358 398 Index Required: Find Spearman's rank correlation coefficient and say whether FTSE Index is a reasonable indicator for the price of the company's share.PAGE 1 -- Consumer Utility Assume both Good X1 and Good X2 cost 52, and Person] has a budget of $24 for the two goods. Assume, given the shape of hisfher indifference curves, Person J most prefers to consume equal units of Goods A and B. 1a. (i) Draw an indifference curve for Person J for goods X1 and X2. In your diagram place Good X2 on the yaxis and Good X1 on the xaxis, and label the indifference curve l1. (ii) Insert a budget line curve into the diagram that reflects the optimal preference of Person] with his/her cui'rent budget. On each axis, indicate the amount of X1 and X2 that Person] is consuming. 1b. (i) Return to la and draw two additional indifference curvesone below the original indifference curve and one above the original indifference curve. Assume the price of Good X1 falls to $1. Make changes to your diagram in (a) above as a result of this price change. 1c. At the new price for good X1, how many units of X1 does consumer] consume? 1d. At the new price for good X1, how many units of X2 does consumer] consume? 1e. Depict the individual demand curve of Person] for Good X1 for quantities demanded at prices 51 and 52. Show numerical values for price and quantity. Part II - Supply and Demand (18 points - 3 points each) There are six separate questions below. Each question begins with a news headline. After you read the headline in bold, please answer the question directly below it. Examine what happens to equilibrium price and equilibrium quantity in the market listed below the headline. In answering these questions, please provide the correct graphical representation of each situation (i.e., in the first question, you should provide a graph for the market for vacations to Hawaii). Identify whether the demand curve or supply curve is impacted in the given market and make sure to explain why the curve would be impacted. Please explain how you came to your answer (the more detail you give the more points you receive). Each question is worth 3 points. 1) Household incomes increased 25% over the last year How does this impact the market for vacations to Hawail? 2) Bad weather leads to a lower than expected harvest of the orange crop How does that impact the market for apple juice at local grocery stores? 3) The State of Connecticut imposes tolls on route 1-95 (the main route used to travel to NYC for many workers) How does this impact the market for train tickets on the Metro-North into New York City? 4) The John Deere Company manufactures a new tractor that allows farmers to harvest their crops in 12 the time it used to take to harvest How does this impact the market for cereal? 5) The U.S. Government mandates that fast food restaurants (like Mcdonald's) have to increase the quality of their beef used in the production of their hamburgers How does this impact the market for McDonald's hamburgers? 6) Meteorologists predict an above average amount of snow for the Northeast United States this coming winter How does this impact the market for snow blowers in the Northeast United States?2. You have a Margin Account. Assume you buy 150 Pfizer (PFE) shares at $70 per share. You put up $6,000 and borrow the rest. a. What is the Margin? b. How would this be represented in the balance sheet? Assets Liabilities and Account Equity Now assume that your margin account requires a maintenance margin of 30%. If PFE is selling for $40, would you receive a margin call? Why? d. If the Price increases to $95 per share, what is the new margin? Will you be having a margin call or not? Why? 3. Define Short Sales. Make sure you explain what a long position and a short position are. a. Now assume that that you short 500 shares of AT&T (T) at $50 per share. Your broker has a 40% initial margin. How does this look in the balance sheet? Assets Liabilities and Account Equity b. Your broker has a maintenance margin of 30%. If the price of the stock falls to $30 per share, what is your new margin? Are you benefited or affected by the price decrease? How do you represent it in the balance sheet? Liabilities and Account Equity 4. You are to decide whether to invest $26,000 in stocks or options for three months. You're looking at Monster Beverage, which is currently selling for $20 per share. You also notice that a call option with a $20 strike price and three months to maturity is available. The premium is $3. Monster pays no dividends. You're considering investing all $26,000 either in the stock or in the call options