MIS382N Homework 1 -Solved

If you feel it necessary you may offer a concise explanation of how you calculated any numbers you are asked to report.  You may insert a comment or type directly into your spreadsheet.

As noted in the popular press government policies on the labeling of food products as “genetically modified” is a controversial topic.  Little is understood in terms of consumer behavior with regards to such labels.  To help us understand consumer behavior in this space, we have collected a choice based conjoint data on consumer preferences.  The attributes and levels for the study are as follows:

Type
Production Method
Price per Pound
Level 1
Tuna
Wild
$13.99
Level 2
Halibut
Farm Raised
$16.99
Level 3
Salmon
Farm Raised/Genetically Modified
$19.99
 

A fractional factorial design was used to develop 9 profiles to be evaluated by consumers.  Consumers offered a binary yes/no decision to the question of would they buy each profile.  A sample of 109 consumers completed the study.  Their data are available in the files fish_preferences.xlsx. 

Using these data please complete the following exercises.

1) Specify a binary logit model of consumer choice.  For your model, treat “salmon” as the baseline type and “farm raised/genetically modified” as the baseline production method.  Let price enter the utility function linearly in tens of dollars (see class notes from conjoint) and include an intercept term in your model.  Using Excel, build the total log-likelihood function and use solver to find the parameter values that maximize the log-likelihood (NOTE:  This is a binary logit model similar to the GMAT exercise done in class.  The utility of buying is a linear function of an intercept and the attributes of the profiles.  The utility of the no buy option is simply zero.  The car example we worked in class on Sept 8 is a more complicated multinomial logit model you do not need for this assignment).  Report your estimated parameters.

2) Using your estimates of the model parameters compute the predicted probabilities for each individual.  

3) Compute the derived importance of each attribute.  Which attribute is most important?

4) Holding production method constant, what is your estimate of the dollar value of tuna relative to salmon and halibut relative to salmon?  Holding type constant what is your estimate of the dollar value of Wild relative to Farm/GMO and Farm relative to Farm/GMO?  How do you interpret these results?

5) Part I.  Assume the following market with four products and a “None” option.

Product
Type
Method
Price
1
Tuna
Wild
$19.99
2
Halibut
Wild
$18.99
3
Salmon
Wild
$15.99
4
Salmon 
Farm
$13.99
None
---
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Using the logit rule to compute the share of respondents predicted to choose each option at the given prices (don’t forget the intercept term for Products 1-4 and recall that price is coded in tens of dollars).  What happens to the share of Farm Raised Salmon (Product 4) if it becomes Farm Raised and Genetically Modified (still priced at $13.99)?  


Part II.  Keep Product 4 as Farm/GMO Salmon at $13.99.  Holding the price of Product 1, Product 2 and Product 4 constant, predict the product shares when the price of Product 3 (the Wild Salmon) varies from $13.99 to $19.99 in increments of $3.00.  Record your answers in Excel in a Table similar to the one below.  Use the table to compute own and cross price elasticities of the product shares.  The elasticities may be computed using the simple arc elasticity formula (i.e. the ratio of the % change in share from $13.99-$19.99 to the % change in price from $13.99 to $19.99 using the midpoint formula to compute the % changes as we did in class).  What do you observe regarding the pattern of cross-price elasticities?  Is this a sensible pattern of price competition in this market?

   Product Shares as a Function of Product 3 Price

Price of Product 3
$13.99
$16.99
$19.99
Product 1
 
Product 2
 
Product 3
 
Product 4
 
None