Number of Competitors As a rule of thumb, the elasticity of demand for a firm's product is propor- tional to the number of firms offering the product. CALIFORNIA MANAGEMENT REVIEW VOL. 50, NO. I FALL 2007 207 A Dashboard for Online Pricing When the number of competing sellers doubles, a firm's elasticity of demand doubles, and its optimal markup declines. To illustrate, consider an e-retailer that is the only seller listing a product on the price comparison site. Based on price experimentation, it determines that the price elasticity is -2. Using the formula for the optimal markup factor, the firm optimally charges a price that is twice its incremental cost. When an addi- tional firm lists on the site, the firm can deduce, without any additional experi- mentation, that its price elasticity has doubled, and that its optimal markup factor has declined to 1.33.(4 points total) Pricing_A_B_test.XlsX on iLearn contains data from an \"AB test\" with different prices for a widget offered by a rm over the internet. The pricing levels chosen in the tests were based on secondary data estimates on price elasticities in the product category, consumer focus groups and discussions among marketing managers and associates in the rm. The variable cost (or incremental cost or marginal cost) for the widget is $1.62 including the cost of click-through fees. The data from the AIR test in the spreadsheet are reproduced below. Sales Price Units $2.79 20,909 52.99 13,205 $3.19 15,994 53.39 14,162 $3.59 12,628 (0.5 points) The firm would also like to have a measure of the price elasticity to use to adjust its pricing in the future in response to changes in the variable cost and to changes in the number of competitors (see the article on "A Dashboard for Online Pricing" and endnotes 6 and 7 in this article). Use the formula in footnote 7 to calculate the elasticity at each data point and average the elasticities. This formula comes from the elasticity formula, E = (AP) () (1 point) An alternative way is to estimate the elasticity after fitting a regression model to the data from the experiment. A regression model that is typically used to estimate the elasticity is to regress the natural logarithm (In for short) of quantity against the natural logarithm of price as follows: such a model is called a log-log model. In(Quantity) = Intercept + 8 * In(Price) In this case, the coefficient of the In(Price) directly gives an estimate of the average elasticity. Thus, the elasticity, E = B. Compute the elasticity by estimating a log-log regression model. ' (For instructions on running a regression model in Microsoft Excel, see, for example: https://www.wikihow.com/Run-a-Multiple-Regression-in-Excel) (0.5 point) Using the elasticity calculated in (b) or (c) above, calculate the optimal markup on cost using the formula in footnote 6. Apply this optimal markup formula to calculate the optimal price using the formula in the article.e. (0.75 point) Should you run further AtB tests to conrm the optimal price? (Hint: You could estimate how much additional prot you might gain by ne-tuning the price through an additional AIB test this could then be compared with the cost of running a test. To estimate the potential prot from ne-tuning the price, estimate the demand at the optimal price that you calculated in (d), and then estimate the prot at that price.) f. (0.5 point) According to the rule of thumb in the article, \"A Dashboard for Online Pricing\