Regression Model

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1.
Qeach brand t=β0+β1*PMinute Maid t+β2*PTropicana t+β3*PPrivate label t+ueach brand t
Q: quantity P: price
By running the above regression model for each brand, we got the following elasticity matrix and the figures for “V” and “C.” Note that we used the average price and quantity for P and Q to calculate each brand’s elasticity. Price Elasticity | Tropicana | Minute Maid | Private Label | Tropicana | -3.4620441 | 0.40596537 | 0.392997566 | Minute Maid | 1.8023329 | -4.26820251 | 0.765331803 | Private Label | 1.3138871 | 1.41197064 | -4.130754362 |

VTropicana = 0.40596537+0.392997566 = 0.7989629
CTropicana = 1.8023329+ 1.3138871 = 3.11621998
VMinute Maid = 1.8023329+0.765331803 = 2.5676647
CMinute Maid = 0.40596537+1.41197064 = 1.81793601
VPrivate Label = 1.3138871+1.41197064 = 2.7258577
CPrivate Label = 0.392997566+0.765331803 = 1.15832937
“V” suggests the vulnerability of each brand to the price changes of other two brands. On the other hand, “C” suggests the clout of each brand to the other brands. For example, the brand that has the highest vulnerability is private label (2.73), which means private label is most vulnerable to the other two brands’ price changes. If Tropicana and private label each depreciate their price by 1%, then the sales of private label will decrease by 2.73%. In contrast, the brand that has the highest clout is Tropicana (3.12), which means Tropicana is the most influential brand of the three. If Tropicana cuts its price by 1%, the sales of Minute Maid and private label will drop by 3.12% altogether.
These figures also show a reasonable, real-life situation. All of “V” and “C” are positive, which means that all of the three brands are mutually substitute goods. If a brand decreases its prices, the other brands’ sales will decrease. If a brand increases its prices, the results will be vice versa. In other words, consumers consider these brands close subsitutes for one another.2.

2 a) Given

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