Please answer the following four questions. The following attachment has a complete problem
A marketing manager at General Mills analyzed weekly sales data at several stores located at Riverforest Illinois for 399 weeks, and estimated the following demand models for 3 brands (Wheaties 18oz, Cheerios 20oz and Honey Nut Cheerios 14oz). Then, consider following 3 demand models. Sales1t =α+β1*price1t++β2*price2t +β3*price3t +ε1t (a) Sales2t =α+β1*price1t++β2*price2t +β3*price3t +ε2t (b) Sales3t =α+β1*price1t++β2*price2t +β3*price3t +ε3t (c) ,where Salesit : Unit sales of brand i at week t priceit : Unit retail price (cent) per oz of brand i at week t i=1: Wheaties 18oz, i=2: Cheerios 20oz, i=3: Honey Nut Cheerios 14oz t : week
1) Estimate three LINEAR demand models using the sales data and report & interpret the regression results including marketing strategies.
2) Using the demand models and estimation results, find an optimal price of Wheaties 18oz when price2t = 20 cents and price3t = 23 cents. Use the unit cost below. Note that variable cost indicates cost (cents) per oz. Wheaties Cheerios Honey Nut Cheerios Unit variable cost 14.7 cents 17.1 cents 18.8 cents
3) Please compare the optimal price you computed and the trend of actual prices in the data.
4) Using the demand models and estimation results, find self-price elasticity of Honey Nut Cheerios 14oz and cross-price elasticity of Honey Nut Cheerios 14oz with respect to Cheerios 20oz, and interpret the results. Use the average prices below. price1t (Wheaties) price1t (Cheerios) price1t (Honey Nut Cheerios) average unit price 18.2 cents 20.4 cents 22.9 cents