Please see attachment, there are problems that I need help to solve them. Anybody could help I would much appreciated!

Good Luck!! 1. (i) Demand function for tickets for a rock concert has been estimated to be ln Q = 3.737 - 1.372 ln P +1.823 ln I where Q denotes number of tickets (in thousands), P the (average) ticket price and I the average income of the concert goers. Determine the values of the price elasticity of demand and the income elasticity of demand. (ii) In a recent study it has been estimated that the own price elasticity of demand for a special type of U.S. manufactured automobile tires is - .75, while the income elasticity of demand is 1.1 and the cross price elasticity of demand with respect to foreign imports is 1.4. The current sales volume for the U.S. manufactured tires is 5 million unites per year. It is anticipated that the price of the foreign imports will rise by 5%. (a) Assuming that average income of the target group of customers will not change, calculate the number of tires that the tire manufacturers will be able to sell if they plan to increase their own price by 3%. (b) According to newly released economic data It is now expected that over the next year the average income of the target group of consumers in the U.S. will grow by 4%. Calculate the amount (%) by which the U.S. tire manufacturers can adjust their price if they wish to increase their sales volume by 8.4% over the initial 5 million units. Assume the same increase in foreign tire prices as above. (iii) Bright Future, Ltd (BF) is a nonprofit foundation providing medical treatment to emotionally distressed children. BF has hired you as a business consultant to design an employment policy that would be consistent with its goal of providing the maximum possible service given its limited financial resources. You have determined that the service (Z) provided by BF is a function of its medical staff input (M) and social worker staff input (S) which is given by: Z = M + .5S + .5 MS - S2 BF's staff budget for the coming year is $1,200,000. Annual employment costs are $30,000 for each social worker staff member (S) and $60,000 for each medical staff member (M). (a) (b) (c) (iv) Using the Lagrangean multiplier approach calculate the optimal (i.e., service maximizing) combination of medical and social worker staff. Determine the optimal amount of service provided by BF. Calculate BF's marginal cost. Explain your answer. Using Excel-Solver verify your answer to (a). (Show your work. Show the spreadsheets in detail. Show the Solver window embedded on the relevant worksheet so that the commands in the Solver window become directly visible and are linked to the cells of the worksheet. To show the solver window, use print screen command on your key board and then create a MS Word document using paste. See The Solver supplement for help.) In year 2014 price of a (500 ml.) bottle of wine made by Richard Mondavi was $14.00. Fifty (thousand) bottles were sold. It was estimated that the own price elasticity of demand for wine of that type was -1.4. Assuming a straight line demand curve, determine the demand equation for Mondavi's wine. Show and explain all your calculations. 2 (i) The production function for a firm is given by q = L.7 K.4 where q denotes output; Land K labor and capital inputs. (a) Determine marginal product of labor. Show whether or not the above production function exhibits diminishing marginal productivity of labor. (b) Calculate the output (or production) elasticity with respect to labor. (c) Determine the nature of the Return to Scale as exhibited by the above production function. Show and explain all calculations. (ii) A firm's production technology is given by the production function q L2K where L represents labor hours, K machine hours and q the amount of output. The market wage and rental rates are, w= $64 and r = $128. The firm is operating in the long run where it can adjust both inputs. (a) Suppose that the firm currently is using twice as many units of labor as capital. Is it minimizing its long run total cost? If so why so and if not why not? Explain. If it is not minimizing its long run cost, how should it adjust its input usage? Explain. Provide appropriate calculations. (b) Suppose that the firm wants to produce 128 units of output. Determine the cost minimizing combination of L and K. Calculate the resulting long run total cost. Show and explain all calculations. (c) Calculate the short run total cost if q =128 and w= $64 and r = $128, but capital, K is fixed at 1. (d) Without assuming a specific numerical production target, but using w= $64 and r = $128 calculate the equation for the long run total cost function (in terms of q). (Hint: Assume that the level of output is q. Using the above w, r values first determine the least cost combinations of L and K) (e) Using Excel- Solver verify your answers to (b) above. (Show your work. Show the spreadsheets in detail. Show the Solver window embedded on the relevant worksheet so that the commands in the Solver window become directly visible and are linked to the cells of the worksheet. To show the solver window, use print screen command on your key board and then create a MS Word document using paste.) (iii) Summit Farms hires unskilled daily workers to pick strawberries in their fields. The actual production depends on the availability of workers and weather related factors. Summit Farms has the following data on the number of workers used, L and the amount of production, q, measured in pounds of strawberries for 15 days. Daily Production Data Day L q 1 5 250 2 7 385 3 8 442 4 6 331 5 6 324 6 8 442 7 10 500 8 11 478 9 12 432 10 9 490 11 10 480 12 10 494 13 8 317 14 7 399 15 8 448 Using Excel's Regression package estimate a production function for Summit Farms which is of the form: q =a L3 + b L2. Provide the detailed regression output generated by Excel. Identify the estimates of the coefficients a and b. Write the equation for the estimated production function. Identify the value of R2 . (a) If you are using a Mac you can use the linest function key for running the regression. (b) Using the estimated function and Excel's charting tool plot the Total Product of Labor (TPL), the Average Product of Labor (APL) and the Marginal Product of Labor Curves. Are these graphs and thus the estimated cubic production function consistent with standard TPL, APL and MPL curves? 4 3. (i) The Write Easy Company manufactures a variety of pens selling for $2.98 each. Sales have averaged 10,000 units per month during the last year. Recently Write Easy's closest competitor, Joy Write Company cut its prices on similar pens from $3.49 to $2.59. As a result Write Easy's sales declined to 8,000 units per month. (a) Calculate the arc cross price elasticity of demand between Write Easy's and Joy Write's pens. (b) If Write Easy knows its own arc price elasticity of demand for its pens to be -2.2, what price would they have to charge in order to restore their monthly sales back to 10,000 units? (Assume that Joy Write maintains its price at $2.59.) Show and explain all calculations. (ii) Dirt Diggers (DD) is an excavating firm that excavates roadside ditches for laying drainpipe. Its output follows the following production function: Q = 10L - .1L2 where L denotes labor hours and Q the length of the ditch in meters. DD hires labor at the going wage rate of $12 per hours. (a) DD has received an offer to excavate 250 meters for a lump sum price of $500. Should it accept the offer? Explain with appropriate calculations. (b) Suppose instead of the previous offer DD is offered as much or as little excavation work at a price of $2.00 per meter dug. Should it accept the offer? If it does, calculate its profit and the optimal (profit maximizing) output (meters dug) and labor usage. (iii) As the manager of an 80-unit motel you know that all units are occupied when you charge $60 a day per unit. Each occupied room costs $30 for service and maintenance a day. You have also observed that for every x dollars increase in the daily rate above 5 $60, there are 2x units vacant. Determine the daily price that you should charge in order to maximize profit. Calculate the number of occupied units. Assuming that fixed cost is $550 calculate optimal profit. (Hint: You may like to determine the demand function first.) (iv) A firm is selling a product with a constant marginal cost of $60. The own price elasticity of demand for the product has been estimated to be -1.5. Calculate the profit-maximizing price that the firm should charge. (v) The domestic demand and supply function for oil for a small country is given by: Qd = 210 - 1.5p and Qs = - 140 + 2p, where p is the price per barrel and Qd Qs are the quantities in million barrels. (a) Use Excel to calculate quantity demanded and quantity supplied for p = $70, 75,80....140 (in $5 increments). Determine the equilibrium price and quantity in absence of any oil import. (b) Assume that OPEC can sell unlimited quantity of oil at $80 per barrel. Using your calculations in (a), determine the equilibrium price, amount of domestic consumption, quantity supplied by domestic producers and the amount of oil import. (Assume that at a given price, the amount of import is the gap between domestic demand and domestic production.) (c) Now, suppose the country's government imposes a limit on the amount of oil that can be imported from OPEC at their price of $80. Given that the limit is set at 35 million barrel, use Excel and the spreadsheet created in part (a) above to calculate the aggregate supply of oil that includes the domestic supply and the import from OPEC. Calculate the domestic price for oil, domestic consumption and domestic production. 6