Assignment:
Q1. A firm is developing a new product. An early introduction (beating rivals to market) would greatly enhance the company's revenues. However, the intensive development effort needed to expedite the introduction can be very expensive. Revenues and costs associated with the new product are given by:
R = 720 - 12t
and
C = 600 - 20t + 0.2t2
where t is the introduction date (in months from now). Some executives have argued for an expedited introduction date, 15 months from now (t = 15). Do you agree? What introduction date would you recommend?
Q2. The Tricities Bus Company is a regional bus line providing transit service between Coquitlam, Port Moody and Port Coquitlam. An analysis of the monthly demand for transit reveals the following demand equation:
Qx = 1,750 - 40Px - 15PC + 30BAI - 1,700S
Where Qx is quantity measured by the number of passengers per month, Px is the price, PC is a price index for connecting bus routes, BAI is a business activity index and S, a binary or dummy variable, equals 1 in summer months, zero otherwise.
Currently Px = 50, PC = 120, and BAI = 175.
(a) Calculate the quantity demanded during the winter month of January if all price-related variables are as specified above.
(b) Calculate the price elasticity of demand in winter for transit services and the cross-price elasticity of demand for transit with respect to the level of business activity.
(c) What price would you recommend the Tricities Bus company charge in the winter months if they were primarily interested in maximizing revenue?
(d) Calculate the quantity demanded during the summer month of August if all price-related variables are as specified above.
(e) Calculate the price elasticity of demand in summer for transit services and the cross-price elasticity of demand for transit with respect to the level of business activity.
(f) What price would you recommend the Tricities Bus company charge in the summer months if they were primarily interested in maximizing revenue?
Q3. The demand for the Bus 207 textbook (QX) is given by the following equation:
QX = 100 - 5.0 PX + 1.5 PY - 2 PZ + 4.7 AX.
where
PX = the price of the textbook, currently selling at $72.00
PZ = the price of the Study guide accompanying the text, selling at $30.00
AX = Advertising for the text, measured in units, and currently at 100
PY = the price of another managerial economics textbook, currently selling at $60.00
(a) The revenues received by an author are frequently set at 15% of the publisher's total revenue. Use price elasticity to determine whether from the author's point of view, the textbook been under priced or overpriced?
(b) By how much would the demand for the textbook change if advertising were increased by 2%?
(c) What is the optimal price of the textbook from the author's point of view?
(d) If the cost per unit of good X to the publisher is $40.00 and the publisher behaves as a monopolist, how many textbooks will be sold and at what price?
(f) As the student consumer, whose interest would you like to see prevail, the author or the publisher?
Q4. Management at the Macho Burrito Hacienda has completed a study of weekly demand for its super-supremo-dos-nacho-double-grande-mucho-muncho burritos. The study revealed that the demand for the four pound cheese-stuffed, bacon-smothered, grease-dripping, colossal-sized macho burrito meal (X) is given by the following equation:
QX = 1,320 -1,000 PX + 700 PT + 7 I + 200 A
where QX = the number of the four-pound macho burrito meals sold
PX = the price of the four-pound macho burrito meals
PT = the price of bacon cheeseburger double-decker tacos
I = per capita income
A = Advertising expenditure
Currently PX = 5, PT = 2, I = 40 and A = 20.
(a) Calculate the elasticity of demand for burrito meals with respect to the price of burritos, the price of tacos, and per capita income.
(b) Should the Macho Burrito Hacienda raise the price of its burrito meals to increase Total Revenue? Why or why not?
(c) Calculate consumer surplus at the Revenue-maximizing price.
(d) If the cost per burrito is $3 and Macho Burrito Hacienda behaves as a monopolist, how many burrito meals will be sold and at what price?
Q12. The demand for good X is given by the following equation:
QX = 10 PX-2.4 PY I1.2 AX 0.001 AY-0.003
where PX and PY, and PZ are the prices of X and Y, I is per capita income, AX is advertising on good X, and AY is advertising on good Y.
(a) Should the price of X be increased or decreased if the firm is interested in maximizing revenue?
(b) Are goods X and Y gross substitutes or complements?
(c) By how much must the price of X change if per capita income decreases by 4% and the goal is to keep QX constant?
(d) Calculate the elasticity of demand for good X with respect to advertising on good X. Interpret your answer. Can you tell whether the firm is spending too much or too little on advertising?
(e) If the manufacturer of good Y stops advertising completely, what would be the impact on demand for good X according to this demand equation?