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 =
Next, plugging the given regression model into the above three equations, we get the following equations: β0+2*β1*PMinute Maid+β2*PTropicana+β3*PPrivate label-0.015 *β1= 0 β0+β1*PMinute Maid t+2*β2*PTropicana+β3*PPrivate label-0.010 *β2= 0 β0+β1*PMinute Maid t+β2*PTropicana+2*β3*PPrivate label-0.008 *β3= 0
The convergent results are as follows: | Price | Quantity | Profit | Tropicana | 0.031378 | 5,702,650 | 93,398 | Minute Maid | 0.022841 | 4,176,415 | 53,628 | Private Label | 0.017059 | 4,155,142 | 37,640 |
Compared to the results from the second time, each price and profit further decreases. This shows that each brand depreciates its price to attain consumers from other brands so that it maximizes its profit.
c) Although this analysis is limited only to three companies, we concluded that it represents optimized decisions for these companies in a real-life situation. This is because of U.S, regulations and the competitive juice markets.
If they cooperate to maximize their profits, they can set higher prices. For instance, if they formed a cartel to maximize their total profits, then the prices and profits would be given as follows. | Price | Quantity | Profit | Tropicana | 0.036924 | 4,322,272 | 94,763 | Minute Maid | 0.028402 | 3,340,483 | 61,473 | Private Label |