# Regression Model Essay

1120 Words5 Pages
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 =…show more content…
The results are shown as the following table. 0 time | Price | Quantity | Profit | Tropicana | 0.032719 | 6,169,469 | 109,315 | Minute Maid | 0.025065 | 4,899,823 | 73,815 | Private Label | 0.019055 | 5,070,952 | 56,061 | b) Given the prices in part a, each brand would change the prices to the ones listed above to maximize their profits. The results of the second set of prices, after maximized again based on the set of prices in part a, are be shown in the following table. 1 time | Price | Quantity | Profit | Tropicana | 0.031718 | 5,820,998 | 97,314 | Minute Maid | 0.022938 | 4,208,201 | 54,447 | Private Label | 0.017376 | 4,300,510 | 40,320 | It shows that each brand depreciated its price to remain competitive in the market, gain consumers from the other brands and to maximize its profit. Based on these prices, we recalculated the optimal prices of each brand so that they can each maximize their profits for a third time. The results are as following. 2 time | Price | Quantity | Profit | Tropicana | 0.031414 | 5,715,162 | 93,808 | Minute Maid | 0.022938 | ,208,201 | 54,447 | Private Label | 0.017376 | ,300,510 | 40,320 | This matrix shows that each brand again drops its price to increase its market share.. The convergent three prices would be calculated by solving the following three equations. dπTropicanadPTropicana = 0 ⋯① dπMinute MaiddPMinute Maid = 0