Bernard, John C.

He, Na

English

Research Papers in Economics

Consistency of Willingness to Pay and Preferences  	

in Auction Experiments  	

Na He & John C. Bernard,  Department of Food & Resource Economics, University of Delaware 	

Experimental auctions are used to determine consumers’ 
willingness to pay (WTP).  The auction mechanism typically 
used is some variation of Vickrey’s second price auction, 
where the weakly dominant strategy for subjects is to bid their  
true value for the goods offered.  It is assumed that subjects 
will submit a higher bid for goods they prefer.  One key 
underlying assumption for consistency between preference 
and WTP is procedure invariance (i.e., this says that ordering 
between two goods for a consumer should be the same 
whether determined by bidding in the auction or by asking 
them which they prefer).    	

Introduction	

Results	

Methods	

Overview of Experimental Auctions	

Scope:	
 	
 6 sessions; 115 subjects;	

	
 	
 	
 6 items auctioned per session; one binding bid	

Dates:	
 	
 June 2009	

Locations:	
 	
 Beijing Normal University, Beijing, China	

Payment:	
 	
 ¥25 (≈ $3) for one hour and a half	

Items:	
 	
 a can Pepsi and a Coca cola (12 oz)	

	
 	
 	
 a pen and a ball-pen	

                             a kg conventional and a kg organic apples	

Auction methods: Fifth price 	

	
	
	
	

Objective	

This study was conducted to investigate whether preference 
violate procedure invariance in experimental auctions and, if 
so, under what conditions the violation occurs. 	

Measuring the consistency was done by asking experimental 
subjects their preference for the commodities being valued 
and then comparing these preferences with their WTP from 
the auctions. 	

Figure 1 The mean bids and the means of expected prices	

Conclusions	

A consumer bidding more for organic apples over conventional does not 
necessary mean the person prefer organic apple. Therefore, the implications of a 
higher WTP must be viewed with care.	

Inconsistencies were found in all trials. These occurred least often in the Pepsi 
and Coca-cola pair.  For pairs with differences in familiarity and expected 
prices, the inconsistencies increased.  The highest frequency of inconsistency 
appeared in the pen and pencils pair suggesting the impact of different prices is 
larger than the different familiarity level in creating the inconsistency 
phenomenon.  	

Table 3 Marginal effects of Tobit model 	

Count  Prefer Coca 
cola 
Prefer 
Pepsi 
Total  
Total % 
           
Bid more 
for Coca 
cola 
30  3  33 
48.39  4.84 53.23 
  
Bid more 
for Pepsi 
1  28  29 
1.61  45.16 46.77 
  
Total  31  31  62 
50  50 
Fisher’s 
Exact Test  <0.0001 
McNemar 
Test 
  
0.3173 
  
Count  Prefer pen   Prefer 
ball-pen 
Total 
Total % 
Bid more 
for pen 
68  32  100 
64.15  30.19  94.34 
  
Bid more 
for ball-pen 
3  3  6 
2.83  2.83  5.66 
  
Total  71  35  106 
66.98  33.02 
Fisher’s 
Exact Test 
0.394 
McNemar 
Test 
   <0.0001    
Count  Prefer 
conventional 
apples 
Prefer 
organic 
apples 
Total 
Total % 
Bid more for 
conventional 
apples 
0  1  1 
0  1  1 
  
Bid more for 
organic 
apples 
20  79  99 
20  79  99 
  
Total  20  80  100 
20  80 
Fisher’s 
Exact Test 
1 
McNemar 
Test 
   <0.0001    
 	
 Entire 
group	

Consistent 	

respondent	

Prefer coca cola	
 N=31	
 N=30	

Mean WTP for 
Coca cola	

2.9445	
 2.976	

Mean WTP for 
Pepsi	

2.4484	
 2.4467	

Matched Pairs t-
Statistic (P-value)	

T=6.23,	
 T=-7.07	

P<0.0001	
 P<0.0001	

Prefer Pepsi	
 N=31	
 N=28	

Mean WTP for 
Coca cola	

2.5177	
 2.5339	

Mean WTP for 
Pepsi	

3.0484	
 3.1536	

Matched Pairs t-
Statistic (P-value)	

T=3.69	
 T=4.15	

P=0.0009	
 P=0.0003	

 	
 Entire group	
 Consistent 	

respondent	

Prefer pen	
 N=71	
 N=68	

Mean WTP for 
pen	

8.0604	
 8.2101	

Mean WTP for 
ball-pen	

4.1858	
 3.994	

Matched Pairs t-
Statistic(P-value)	

T=-11.73	
 T=-15.29	

P<0.0001	
 P<0.0001	

Prefer ball-pen	
 N=35	
 N=3	

Mean WTP for 
pen	

7.9714	
 3	

Mean WTP for 
ball-pen	

4.6771	
 5.0667	

Matched Pairs t-
Statistic(P-value)	

T=-7.37	
 T=1.62	

P<0.0001	
 P=0.2460	

 	
 Entire 
group	

Consistent 	

respondent	

Prefer conventional 
apples	

N=20	
 N=0	

Mean WTP for 
conventional apples	

3.195	
 0	

Mean WTP for 
organic apples	

5.32	
 0	

Matched Pairs t-
Statistic (P-value)	

T=6.4039	
 N/A	

P<0.0001	

Prefer organic apples	
 N=80	
 N=79	

Mean WTP for 
conventional apples	

3.137	
 3.0501	

Mean WTP for 
organic apples	

5.3151	
 5.3191	

Matched Pairs t-
Statistic (P-value)	

T=9.5426	
 T=10.70	

P<0.0001	
 P<0.0001	

 	
 Pepsi	
   Coca cola	
  Pen 	
   Ball-pen	
  Conventional	
  Organic 
apple	
 Apple	

Familiarity	
 -0.2355	
 -0.2029	
 0.2079	
 0.0496	
 -0.2899	
 -0.0011	

Desirability	
 0.3200	
 0.3265	
 0.1720	
 0.2154	
 0.2254	
 0.3507	

Price	
 n/a	
   n/a	
   0.5919	
   0.6525	
   0.8471	
   0.586	

   5% significant level 
   10% significant level 
Table 2 Mean WTP for Entire and Consistent Respondents	

a) Coca cola and Pepsi 	

b) Pen and Ball-pen	

c). Conventional and Organic Apples	

Table1 Contingency Analysis	

a) Coca cola and Pepsi	

b) Pen and Ball-pen	

c) Conventional and Organic Apples	

)P
Fisher’s Exact 
Test	

no relationship between responses 
to the preference and bids. 	

McNemar test	
 the probabilities in the two-by-two 
table satisﬁed symmetry. 	


Consistency of Willingness to Pay and Preferences in Auction Experiments

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Research Papers in Economics