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...

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
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Q5.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 + 0.2t2where 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?Q6.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 - 1,700SWhere 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...

Solution

David answered on Dec 20 2021
Q5.
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?
The introduction date should be such, that maximizes the difference between revenue and cost i.e. that maximizes profit. This would happens at a point where marginal revenue (MR) equals marginal cost (MC)
MR = dR/dt = -12
MC = dC/dt = -20 + 0.4t
MR = MC implies -12 = -20 + 0.4t, implies profit maximizing introduction date t* = 20
So the optimum introduction date should be 20 months (t=20) because here profit gets maximized and hence the claim of some executive that introduction date should be 15 months (t=15) is inco
ect.
Q6.
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.
Cu
ently 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.
This is winter, so value of S = 0
Other values are: Px = 50, PC = 120, and BAI = 175
Putting all these values in the estimated demand function, we get quantity demanded during the winter month of January as: Qx = 1,750 – 40*50 – 15*120 + 30*175 - 1,700*0 = 3200
(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.
From demand equation, dQ/dPx = -40 and dQx/dBAI = 30
And Px = 50, Qx = 3200 (in winter) and BAI = 175
So, price elasticity of demand = (dQ/dPx)*(Px/Qx) = (-40)*(50/3200) = -0.625
And cross price elasticity = (dQ/dBAI)*(BAI/Qx) = (30)*(175/3200) = 1.640625
(c) What price would you recommend the Tricities Bus company charge in the winter months if they were primarily interested in maximizing revenue?
In winter, S = 0. Also we have given PC = 120, and BAI = 175
So putting these values in estimated demand curve, we get simple demand curve as:
Qx = 5200-40Px
Total revenue (TR) = Px*Qx = 5200Px-40Px^2
For revenue maximization: dTR/dPx = 5200-80Px = 0, solving this we get revenue maximizing price (in winter) as: Px* = 65
(d) Calculate the quantity demanded during the summer month of August if all price-related variables are as specified above.
This is summer, so value of S = 1
Other values are: Px = 50, PC = 120, and BAI = 175
Putting all these values in the estimated demand function, we get quantity demanded during the summer month of August as: Qx = 1,750 – 40*50 – 15*120 + 30*175 - 1,700*1 = 1500
(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.
From demand equation, dQ/dPx = -40 and dQx/dBAI = 30
And Px = 50, Qx = 1500 (in summer) and BAI = 175
So, price elasticity of demand = (dQ/dPx)*(Px/Qx) = (-40)*(50/1500) = -1.33333
And cross price elasticity = (dQ/dBAI)*(BAI/Qx) = (30)*(175/1500) = 3.5
(f) What price would you recommend the Tricities Bus company charge in the summer months if they were primarily interested in maximizing revenue?
In summer, S = 1. Also we have given PC = 120, and BAI = 175
So putting these values in estimated demand curve, we get simple demand curve as:
Qx = 3500-40Px
Total revenue (TR) = Px*Qx = 3500Px-40Px^2
For revenue maximization: dTR/dPx = 3500-80Px = 0, solving this we get revenue maximizing price (in summer) as: Px* = 43.75
Q7.
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, cu
ently 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 cu
ently at 100
PY = the price of another managerial economics textbook, cu
ently 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...
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