INDIVIDUAL ASSIGNIVIENT Due on Canvas by 1 PM on April 17 (Monday), 2023; No extensions allowed (This assignment must be answered on an individual basis without any consultation with others) The store manager at the Clayton Schnucks store has estimated Scan*Pro demand models for 2 competing peanut butter brands -- Skippy, Peter Pan -- using weekly scanner data over the past 2 years. The estimated demand models are as shown below. Ln (Qskipoy) =2.99 - 4.55 * In (Pskippy) + 0.13 * In (Ppeterpan), Ln (O.PeterPan) =2.48 +0.16 * In (PSkinpv] 4.09*In (PPelerPan); where Q refers to weekly demand (in units sold), and P refers to weekly price (in $). 1. Suppose you are the store manager at the Clayton Schnucks store. If Skippy and Peter Pan are selling their brands to your store at wholesale prices of $0.54 and $0.58, respectively, what retail prices must you set for the 2 brands at your store? What would be your resulting retail profits in the peanut butter category? Which brand accounts for the greater share of this retail profit? (Hint: Assume that your objective is to maximize your retail profit from the peanut butter category). [4 POINTS] 2. Suppose, instead, that you are the brand manager for Peter Pan. Your marginal cost of production for Peter Pan is $0.33. Taking the calculated retail prices in Q1 which the Clayton Schnucks store sets for your brand and your competing brand, calculate your resulting brand profit as a manufacturer from the Clayton Schnucks store. Is this larger or smaller than the retail profit that Clayton Schnucks obtains from your brand? [2 POINTS] 3. Suppose that you are still the brand manager for Peter Pan and that you want to change your wholesale price of Peter Pan from $0.58 to some other value. Assume that the retailer uses the same percentage mark-up over your wholesale price, as solved under Question 1, to set the retail price for your brand. Under this assumption, what wholesale price must you charge the retailer? What is your resulting profit? By what % is this higher than the profit calculated in Q2?7 (Hint: Assume that Skippy's wholesale price remains at their current value of $0.54, and that the Clayton Schnucks store's retail price for that brand remains at the calculated value in Q1; assume further that your objective is to maximize your brand profit). [4 POINTS] Suppose that you are still the brand manager for Peter Pan. You suddenly realize that Skippy will not stay put if you changed your wholesale price as calculated in Q3. It will change its wholesale price in order to optimally respond to your new wholesale price. Given its changed wholesale price, you will further change your wholesale price as an optimal response to its changed wholesale price, and so on. Where will the 2 wholesale prices finally settle down? In this calculation, assume that the retailer uses a percentage markup over the wholesale price, as solved under Q1, to set the retail price for each brand. Also assume that the marginal cost of production for Skippy is $0.31. (Hint: Assume that the objective of each brand manager is to maximize their brand profit). [5 POINTS] Good Luck