1. (i) Demand function for tickets for a rock concert has been estimated to be

ln Q = 2.327 - 1.015 ln P +1.215 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.

(6 points)

(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 units 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%.

(8 points)

(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.

(8 points)

(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 + 2S + MS - S²

BF's staff budget for the coming year is $900,000.Annual employment costs are $60,000 for each social worker staff member (S) and $120,000 for each medical staff member (M).

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

(28 points) (b)Calculate BF's marginal cost.Explain your answer.

(8 points) (c)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 use MS Word document using paste. See the Solver supplement for help.)

(10 points)

(iv)In year 2018 price of a (750 ml.) bottle of Port made by Taylor Fladgate of Portugal was 30.00.100 (thousand) bottles were sold. It was estimated that the own price elasticity of demand for port of that vintage was -1.2. Assuming a straight-line demand curve, determine the demand equation for Taylor's port.

Show and explain all your calculations.

(12 points)