You have been retained by a regional food marketer, FoodKing, to forecast the demand for small cakes that are mass-produced and marketed under the name Johnny's Pies. To assist with your analysis, you are provided with data that was collected for 8 consecutive quarters and 6 geographic markets.
(a) Estimate a regression model that expresses sales as a function of price, income and competitor's price and population? Once you have estimates the regression model, (a) provide a clear interpretation of the "R2" and (b) the statistical significant of the overall regression. Be sure to explain if the overall regression is statistically significant at a 5% level and how you know that.
b) Can you provide a clear, concise interpretation for the slope coefficient on price?
Is that coefficient significantly different from zero? How do you know that?
c) Can you provide a clear, concise interpretation for the slope coefficient on income?
d) FoodKing is considering entering a new market. In this market, the population is
2,650,000, the average (or per capita) income is $42,500 and the competitor's product sells for $4.85. Using this regression model, if you price your product at $5.25, how many pies will you sell?
If you price your product at $5.25, what would be the price elasticity of demand for your product at that price? Is this elastic or inelastic? If you raised the price of the product by a very small amount, would the profit rise or fall?
(f) At what price would you maximize the TOTAL REVENUE that the firm receives?
Assume that if your firm enters the market, is will be able to produce pies at a constant marginal cost of $3.25 per pie, at what price would it maximize PROFITS? Do you need to know the fixed cost to answer this question? What is the price elasticity of demand at that price?
) One of your assistants notes that market that you are considering entering is located in the southern part of the nation and asserts that "everyone knows that southerners eat lots of snack cakes." You note that in your data set, Atlanta and Dallas are the only two cities that are in the "South" census district. Can you test you assistant's hypothesis that "southerners eat lots of snack cakes" - is she correct?