Question 2 (30 points) You are advising Procter and Gamble (P&G), who produces Tide Laundry detergent. P&G's main competitor is Unilever, who produces the laundry detergent Wisk. P&G wants you to model consumer choices in the laundry detergent market to help it think about how to implement its marketing strategy. You decide to use the logit model to model consumer choice. Suppose that you begin by writing down a choice model where consumers have 3 choices. They can purchase Tide, or purchase Wisk. or purchase nothing (they don't purchase both products). Consumer utility for each choice is: Tide: &; + apr + g Wisk: Sy + apw + aw Nothing: 0 + g4 The variables pr and pw are the prices of Tide and Wisk, respectively. You may assume that you as the researcher observe these prices. a) What does the parameter @ measure? How do consumer choices change as a gets larger in magnitude? (Note that a is always negative). (5 points) b) Provide an interpretation of the model parameters dr and dw. (5 points) For part ), assume that the total market size for laundry detergent is 1 million units. That is, assume that if Tide's market share is sr, its quantity sold in millions of units is Qr = sr. c) Suppose you have collected data on consumer purchases and the prices of both products, and you estimate the logit model described above. You use MEXL to produce the output which is as follows: Table 2.1: Logit Model Estimates for Laundry Detergent Coefficient Estimate | Standard Error t-stat Price -2.01 0.65 3.09 &r 0.56 0.12 4.67 Sw 0.33 0.06 5.5 Suppose that you observe that the price of Wisk is 0.5, and that Tide's price is 0.5, and the marginal cost of producing both Tide and Wisk is 0.1. Suppose that Tide wants to use the logit model to determine its optimal price, under the assumption that Wisk's price does not change. Tide is considering choosing price in increments of 0.25 (so that Tide's price has to be 0, 0.25, 0.5, 0.75, 1, 1.25, etc). Fill in the table below, and identify Tide's optimal price. (15 points) Page 4 of 25 Tide Price Tide Units sold (Millions) Tide Profit (Millions) 0 0.25 0.5 0.75 1 1.25 d) Suppose that you collect some additional data on consumer income, I, which you wish to incorporate into your logit model. Suggest a logit model specification that could incorporate income. (5 points)