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Demand Estimation Assignment - iScream Ice Cream Co.

iScream is a Chicago start-up that sells ice cream in several mobile ice cream trucks. The main innovative feature of their business is the implementation of a smart phone app that allows customers to locate trucks and request service. iScream has been in business for a little over a year, and offers just two products: regular vanilla ice cream cones and organic, low-fat ice cream cones (each with several toppings that are available at no extra cost). Based on your previous recommendation, the firm has frequently (for a month at a time) experimented with changing the prices of each of their products in eightequally-populated regions of the city throughout the first year, and has kept monthly data on their sales and prices of both products. They would now like you to help them gain some insights from the data.

While you know relatively little about the ice cream business, you are well aware that factors other than prices are likely to affect demand for a product. Because, through the app, they have information on time and location of sale, you are able to get data on the average household income (in thousands of $) in the region of sale, as well as the average daily high temperature during the month of sale.

The available data can be found in the excel file, "iScream_data.xlsx". Your goal is to carry out a multiple regression analysis of the data (using Excel), with particular focus on estimating the price elasticities of demand for both the firm's products. Your maindeliverable is one of the following (your choice), outlining your method of analysis, findings and recommendations:

To help you in doing this, please carry out the following steps and answer the associated questions (you will turn this inin addition to the presentation/report. Your presentation/reportis likely tocontain only some of the following results, with more of an emphasis on making recommendations informed by your results):

i)Begin by looking at the relationship between each product and its own price. Forbothproducts, do/answer the following:

a. First plot create scatter plot of price (on the vertical axis) and quantity sold (on the horizontal axis).

b. Is there a negative relationship between quantity sold and the product's price? To help you decide, insert a trend line into each graph and display the equation of the line. This is a crude measure of the inverse demand curve.

c. Provide an economic interpretation of the slope of these lines.

d. Now determine the equation for the demand function, with Quantity (Q) as the dependent variable and price (P) as the explanatory variable (as opposed to the inverse demand function, with P as the dependent variable and Q as the explanatory variable, graphed above). We'd also like to assess the reliability of the estimated slope parameter. Since the trendline option doesn't provide standard errors, use Excel's Regression tool(see section 3.3, page 67, of your textbook as an example). If this is not already installed, do so by File>Options>Add-Ins. After adding the Analysis ToolPak, "Data Analysis" should appear under the Data tab in Excel. Click on Data Analysis and then Regression. (Note that you can alternatively use the LINEST command.) Using the output , write the demand equation for each good. You can put the standard errors in parentheses below the parameter estimates.

e. Provide an economic interpretation of the slope coefficients. Given the standard errors, are these coefficient estimates statistically significant at the 5% significance level? Based on the R-squared statistic from each regression, for which product does price explains more of the variation in sales?

f. For which product are consumers more responsive to changes in the price? To quantify their responsiveness, calculate the price elasticity of demand for each product using the estimates from part d (see equation 3.6 in the textbook). As you know, elasticity will vary along the linear demand curve, so you'll need to pick a point at which to calculate the elasticities. Choose the product's average Q and average P in the dataset. Interpret these elasticities. Is demand for either product elastic or inelastic?

ii)You know that demand for one product is not only influenced by its price, but also the price of the other product, among other variables. These missing explanatory variables could explain at least part of the noise in your graphs above. To include more than one variable in estimating demand you will need to use the Regression tool. For both goods, do/answer the following:

a. Carry out a multiple regression using linear specification, with quantity as the dependent (left-hand side) variable and own price, other good's price, income, and temperature as explanatory (right-hand side) variables.

b. How do the estimated own-price coefficients compare to those estimated previously without other variables included? Has the statistical significance changed for either good? What is the R-squared?

c. The summer is fast approaching, and experts are disagreeing over how hot the summer is going to be. Some are forecasting an unusually hot summer, with average high temperatures predicted to reach 90 degrees in July. Others are predicting an unusually cool summer, with an average high temperature in July of only 78. The owners of iScream would like to know how this difference in possible temperatures will affect their sales. At the averages of all other variables, use the regression estimates to predict the number of units sold in a month of each good under two scenarios: 1) the monthly high averages 90 degrees; 2) the monthly high averages 78 degrees. Note that because the data are in monthly sales by region (of which there are 8), you'll need to multiply the number of units predicted from the regression equation by 8 in order to get total predicted units sold in a month.

d. Calculate the (own-price) elasticities at the average quantities again using the coefficient estimates. The owners of iScream are interested in knowing what would happen to revenue from their original ice cream cones if they increase its price slightly from the average price of the good in the data (holding everything else constant). Based on the estimated elasticity, would revenue increase, decrease, or stay about the same? Similarly, they are interested in knowing how revenue from their organic product would change if they were to increase its price slightly from the average (holding everything else constant). Would revenue increase, decrease, or stay about the same?

e. Are the goods normal or inferior goods? Calculate the income elasticity of demand for both goods, at the average income and quantity in the dataset.

f. Are the goods substitutes or complements? For which good are sales more sensitive to the other good's price? Calculate the cross-price elasticities at the average price and quantity. Interpret these elasticities.

iii) Prepare either a short written report or a short PowerPoint presentation that summarizes the results from your analysis. I'm flexible in terms of the style you present the results, but try to make your points concise. You may present graphs or small tables in addition to text and bullet points. Also keep the following in mind:

-You may include any (or all, if you can present it concisely) of the results asked for above.

-In addition to knowing specific numbers (of elasticities, for example), they are interested in hearing about how your results might inform their pricing strategies (or other strategies).

-You can create other statistics from the data if you like, but this is not required.

-They are interested in further refining their demand model, so you might suggest to them additional variables that you think should be included, whether they are available now or would need to be collected going forward.

-Finally, they are interested in expanding their business to Memphis, TN. Aside from population differences (ie., equalizing population within regions across the two cities), indicate to them how and why you think quantity demanded may or may not differ between the two cities (for each product). They would also appreciate any other suggestions as to how they might approach the Memphis market, either in terms of pricing or otherwise. (You can be creative here.)