Question

A.4 Confidence Intervals Question 3: You are a manager in charge of monitoring cash flow at Toyota. You must determine how a planned 2 percent increase in the price of the Toyota Prius in 2010 will affect Toyota's overall revenues from both the Toyota Prius and the Toyota Corolla So, you collect monthly data on the prices you charged in the past on the Prius and Corolla, and on the demand for the Prius and Corolla and determine the following regression lines: In(RQ) 9-0.2 In(RP)0.1 In(CP) In(CQ)4-0.5 In(CP)0.8 In(RP) for variables RQdemand quantity for the Prius, RPprice for the Prius, CQ demand quantity for the Corolla CPprice for the Corolla You also collect data on revenue, and find out that in 2009, Toyota earned about $200 million from sales of the Prius about $100 million from sales of the Corolla a) What is your estimate of how the planned 2 percent increase in the price of the Toyota Prius in 20010 will affect Toyota's overall revenues from both the Toyota Prius and the Toyota Corolla? b) If the parameter estimate of the own price elasticity of demand for the Toyota Prius has a 95% confidence interval of-1 to-01, then compute the upper and lower bounds on the 95 percent confidence interval for how the planned 2 percent increase in the price of the Toyota Prius in 20010 will affect Toyota's overall revenues from both the Toyota Prius and the Toyota Corolla Answer to Question:

Answer 1

a)The regression lines imply

• the own price elasticity of demand for the Prius is -.5

• the cross-price elasticity between the demand for the Corolla and the Price of the Prius is +0.1 (the two models are gross substitutes).

Using the-change-in-revenue formula for two products, the estimate of much should you change the price of the Toyota Prius next year so that Toyota’s overall revenues from both the Toyota Prius and the Toyota Corolla will increase by $440,000 is:

$440,000= ∆R = [$200M(1-.5) + $100M(0.1) ] x %∆price = [$110M] x %∆price. So %∆price = $0.44M/$110M = 0.004

So, the price of the Toyota Prius next year should increase by 0.40 %

b) For the confidence interval, insert -1 and -0.4 into the change in revenue formula in the place of the own price elasticity of demand for disposable cameras:

For elasticity -1,

$440,000= ∆R = [$200M(1-1) + $100M(0.1) ] x %∆price

= [$10M] x %∆price.

So %∆price = $0.44M/$10M = 0.044

So, the price of the Toyota Prius next year should increase by 4.40 %

For elasticity -0.4,

$440,000= ∆R = [$200M(1-.4) + $100M(0.1) ] x %∆price = [$130M] x %∆price.

So %∆price = $0.44M/$130M = 0.00338

So, the price of the Toyota Prius next year should increase by 0.338 %.

So the 95 percent confidence interval for how much you should change the price of the Toyota Prius next year so that Toyota’s overall revenues from both the Toyota Prius and the Toyota Corolla will increase by $440,000 is that the price of the Toyota Prius next year should increase between 0.338 % and 4.40 %