A manufacturer of cosmetic products, called Cosmetic International, is using a randomized controlled trial (RCT) to...

   

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A manufacturer of cosmetic products, called Cosmetic International, is using a randomized controlled trial (RCT) to estimate the price elasticity of the demand for a new line of facial products, called Cl-Face. This elasticity measure shows how much, say, a 1% increase in their prices would affect the demand for Cl-Face. They model the demand facing them, Qx (measured in number of Cl-Face item sold online and in-person), as a function of their prices, Px (measured in dollar price per Cl-Face item), and the price of three set of products that are produced by their rivals but are similar to the newly launched set: P₁, P2, and P3. Here is the population regression model that they used: LnQx=c+b*LnPx+a₁ *LnP₁+a2* LnP2+a3* LnP3+u Also, since the above model is log-linearized, parameter b is the price elasticity of demand for the new facial products, Cl-Face. It shows how much, say, a 1% increase in the prices that are charged by Cosmetic International would affect the demand for Cl-Face. Also, parameters a₁, a2, a3 represent the cross price elasticities. For example, a₁ shows how much, say, a 1% increase in the price of the similar products that are produced by their first rival, Europe Cosmétique, would affect the demand facing Cosmetic International. The table below summarizes the estimation results: Parameter C b a₁ a2 a3 Coefficient 0.012 -0.601 0.023 0.173 0.052 SE 0.001 0.150 0.097 0.026 0.019 95% CIE LowerLimit 0.010 -0.898 -0.169 0.122 0.014 95% CIE UpperLimit 0.014 -0.304 0.215 0.224 0.090 The results suggest that a 1% increase in price of Cl-Face products would lower the demand for them by about 0.6%. Also, the confidence interval estimation for parameter b does not include zero, suggesting that the effect is statistically different from zero (and hence significant). With than in mind, it is your job to explore the results for the cross price elasticities. Choose the correct statement: All other variables being kept constant (typically at their mean), a 10% increase in P2 will increase Qx by about 2%. Even when other variables vary (typically up to one standard deviation), a 10% increase in P2 will increase Qx by about 2%. ● All other variables being kept constant (typically at their mean), a 10% increase in P2 will increase Qx by about 0.2%. Even when other variables vary (typically up to one standard deviation), a 10% increase in P2 will decrease Qx by about 2%. All other variables being kept constant (typically at their mean), a 10% increase in P2 will reduce Qx by about 2%. Even when other variables vary (typically up to one standard deviation), a 10% increase in P2 will increase Qx by about 0.2%. All other variables being kept constant (typically at their mean), a 10% increase in P2 will reduce Qx by about 0.2%. Even when other variables vary (typically up to one standard deviation), a 10% increase in P2 will decrease Qx by about 0.2%. A manufacturer of cosmetic products, called Cosmetic International, is using a randomized controlled trial (RCT) to estimate the price elasticity of the demand for a new line of facial products, called Cl-Face. This elasticity measure shows how much, say, a 1% increase in their prices would affect the demand for Cl-Face. They model the demand facing them, Qx (measured in number of Cl-Face item sold online and in-person), as a function of their prices, Px (measured in dollar price per Cl-Face item), and the price of three set of products that are produced by their rivals but are similar to the newly launched set: P₁, P2, and P3. Here is the population regression model that they used: LnQx=c+b*LnPx+a₁ *LnP₁+a2* LnP2+a3* LnP3+u Also, since the above model is log-linearized, parameter b is the price elasticity of demand for the new facial products, Cl-Face. It shows how much, say, a 1% increase in the prices that are charged by Cosmetic International would affect the demand for Cl-Face. Also, parameters a₁, a2, a3 represent the cross price elasticities. For example, a₁ shows how much, say, a 1% increase in the price of the similar products that are produced by their first rival, Europe Cosmétique, would affect the demand facing Cosmetic International. The table below summarizes the estimation results: Parameter C b a₁ a2 a3 Coefficient 0.012 -0.601 0.023 0.173 0.052 SE 0.001 0.150 0.097 0.026 0.019 95% CIE LowerLimit 0.010 -0.898 -0.169 0.122 0.014 95% CIE UpperLimit 0.014 -0.304 0.215 0.224 0.090 The results suggest that a 1% increase in price of Cl-Face products would lower the demand for them by about 0.6%. Also, the confidence interval estimation for parameter b does not include zero, suggesting that the effect is statistically different from zero (and hence significant). With than in mind, it is your job to explore the results for the cross price elasticities. Choose the correct statement: All other variables being kept constant (typically at their mean), a 10% increase in P2 will increase Qx by about 2%. Even when other variables vary (typically up to one standard deviation), a 10% increase in P2 will increase Qx by about 2%. ● All other variables being kept constant (typically at their mean), a 10% increase in P2 will increase Qx by about 0.2%. Even when other variables vary (typically up to one standard deviation), a 10% increase in P2 will decrease Qx by about 2%. All other variables being kept constant (typically at their mean), a 10% increase in P2 will reduce Qx by about 2%. Even when other variables vary (typically up to one standard deviation), a 10% increase in P2 will increase Qx by about 0.2%. All other variables being kept constant (typically at their mean), a 10% increase in P2 will reduce Qx by about 0.2%. Even when other variables vary (typically up to one standard deviation), a 10% increase in P2 will decrease Qx by about 0.2%.

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