During an initial product release, Oasis released the Tranquility 5000 on a per-week basis to gather demand data at a variety of price points. From the raw data, a linear regression model is used to determine the demand function. However, before running the regression, it is necessary to first …show more content…
Using this demand function, and the Price Elasticity of Demand Function E(p) (see equation 2), the price that Oasis can charge is estimated by setting the function equal to 1. The elasticity function is set equal to 1 because demand is considered “unit elastic” at a value of 1, meaning that if more is charged, the raise in price would not offset the loss in demand, and total revenue would decrease. Conversely, if the price is lowered, the raise in demand would not offset the loss in price per unit, and total revenues would decrease. After solving for p in the Elasticity Function, the unit elastic price that Oasis can charge for the Tranquility 5000 is …show more content…
Their data is also given on a per-week basis to allow for an accurate comparison between the supply and demand models. As with demand, it must first be determined if there is a relationship between supply and price before running the regression. A scatterplot is shown is figure 2 with a best-fit line that clearly shows a linear trend. The trend is positive this time, showcasing the tendency for Oasis to produce a greater supply as the price point increases. From the data, both ANOVA and coefficient tables are produced (see tables 3 & 4). The model is found to explain 85% of the variance in price with a standard error of only 1.97. Additionally, a significant relationship is determined at the ⍺ = .05 level, t(108) = 24.40 with the resulting p < .0001. Again, given the statistically valid relation between supply and data, it is appropriate to use the weekly Supply Function S(p) given by the data (see equation