The Value of Free AN INVESTIGATION INTO THE RATIONALITY OF INDIVIDUALSBY: JOEY WACHTVEITL, JOSH TIBBITTS, AND CHRIS FITZGERALD

Consumer Theory: Completeness

Consumers reveal preferences through purchase habits

Consumers prefer certain goods over others A > B, A < B, or B = A Our study challenges completeness in

consumer theory

Study Design

12 replications 2 Factors: Chocolate and Price Chocolate: White Chocolate, Milk Chocolate,

Dark Chocolate Prices: ($0.25, $0.01) and ($0.24, $0.00)

What is the Value of Free?

If there is no interaction between type and price then there is no extra value for free goods.

Conversely, if there is an interaction between factors, then there is an extra value for free goods.

Ho: There is no interaction between the price and type of chocolates.

Ha: There is an interaction between the price and type of chocolates.

Data Collection Each of us were randomly assigned a number between 1 –

3 and each combination 1 – 12. We used a random generator to then assign four of the

combinations to each of us. Sold our chocolates at different locations across campus, 1

hour for each combination. Participants could only purchase one chocolate We had three different flavors (white, milk, dark) Two types, truffle and kiss Our response was the number chocolates purchased In total we had 144 people participate.

Factor Structure

Design

We decided to use a Randomized block design [2] Two way factorial for this experiment.

Descriptive Statistics

Descriptive Statistics Continued

Inferential Statistics

Inferential Statistics Continued

leveneTest(choco$Sold, choco$Type, center = mean)Levene's Test for Homogeneity of Variance (center = mean)     Df F value Pr(>F)group  1  0.1471  0.705     22               

leveneTest(choco$Sold, choco$Price, center = mean)Levene's Test for Homogeneity of Variance (center = mean)     Df F value Pr(>F)group  1  1.5409 0.2276     22              

By these levene tests we fail to reject the null so the variances are not equal.  We tried to do various transformations (log, sin, cos and inverse) none of them improved the variance issues. We decided to move forward and used a 0.01 level of significance for our tests

Inferential Statistics Continued

Inferential Statistics Continued

Interaction Ho: There is no interaction between Price and Type Ha: There is

an interaction Test Statistic  F=9.430 Degrees of Freedom  Num df=6   Den df=48 P-value =0.00659 Since the P-value is less than 0.05 so we would reject the null

hypothesis Therefore, we have sufficient evidence that there is an

interaction between type and price

Inferential Statistics Continued

Based on the results we see that the only significance was with the interaction, which was what we were interested in so we were happy to see that.

Outcome

Sufficient evidence suggests a difference in purchase ratios, with respect to price.

Individuals place extra value on free items.

Implications on Economic Assumptions

Fundamental assumption in economics are that individuals act rationally.

With price difference of $0.24 for both price points, purchasing ratio’s should not change.

Is the fundamental assumption incorrect?

Experiment Shortcomings

We lack the ability to measure marginal utility for each consumer. The variances of high prices and low prices are unequal. A greater number of observations would improve our study.