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Lagrangean Multiplier Approach Assignment | Homework For You

1. (i) Demand function for air travel between the U.S. and Europe has been estimated to be ln Q = 2.737 – 1.247 ln P +1.905 ln I where Q denotes number of passengers (in thousands) per year, P the (average) ticket price and I the U.S. national income. Determine the price elasticity and income elasticity of demand.

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(ii) It has been estimated that the price elasticity of demand for U.S. manufactured automobiles is -1.2, while the income elasticity of demand is 2.0 and the cross price elasticity of demand with respect to the foreign automobiles is 1.5. The current volume of sales for U. S. manufactured automobiles is 10 million per year. It is expected that over the next year the average income of the consumers in the U.S. will increase by 2.5 percent. It has been determined that the price of the foreign imports will increase by 6% over the next year. By how much should the U.S. automakers adjust the price of their automobiles if they wish to increase the volume of their sales by 9.2% next year?

(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 sound service 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 service staff member (S) and $60,000 for each medical staff member (M).

(a) Using the Lagrangean multiplier approach calculate the optimal (i.e., service maximizing) combination of medical and social staff. Determine the optimal amount of service provided by BF. (32 points)

(b) Calculate BF’s marginal cost. Explain your answer.

(c) Using Excel-Solver verify your answer to (a).

(Show your work. Show the spreadsheets in detail. Provide print outs with Solver window. To print the solver window, use print screen command on your key board and then create a MS Word document using paste.) (iv) The own price elasticity of demand for a pack of cigarettes is estimated to be -.4. Current price and consumption are $4.00 and 2 million units per year. Assuming a linear demand relationship determine the demand equation for cigarettes. Show all your calculations. Get Economics homework help today

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