Question

1.

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

ln Q = 3.737 - 1.518 ln P +1.213 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 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%.

(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) 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.

(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. 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.)

(iv) In year 2016 price of a (750 ml.) bottle of wine sold by Richard Mondavi was $20.00. Fifty

(thousand) bottles were sold. It was estimated that the own price elasticity of demand for wine

of that type was -1.6. Assuming a straight line demand curve, determine the demand equation

for Mondavi's wine.

Show and explain all your calculations.

Answer 1

1.

(i) price elasticity of demand is calculated as

price elasticity of demand is -1.518 which means when price increases by 1%, on average quantity demanded decreases by 1.518%

Similarly, income elasticity is calculated as

the income elasticity is 1.213 means when income increases by 1%, on average quantity demanded increases by 1.213 %, ceteris paribus.

(ii)

(a) assuming average income is constant, own price elasticity is -0.75 means if price increase by 1% then quantity demanded decreases by 0.75%.

If the price of the tire by manufacturer increases by 3 %, then on average, number of tires that the tire manufacturer will be able to sell will be 2.25%.

(b) if average income increase by 4% and income elasticity is 1.1 implies an increase in quantity demanded is 4.4%

To measure the increase in sales by 8.4% implies an increase in the number of tires is 12.8% and price elasticity by 0.75 implies that percentage change in price is 17.067%