Experiment with an Auction to create a Demand Function
36
Experiment with an Auction to create a Demand Function Berufsakademie Eisenach Staatliche Studienakademie Thüringen University of Cooperative Education Prof. Dr. Stephan Rometsch
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Experiment with an Auction to create a Demand Function. Berufsakademie Eisenach Staatliche Studienakademie Thüringen University of Cooperative Education. Prof . Dr. Stephan Rometsch. Demand Function. EXPERIMENT. Auctions and the Theory of Demand - PowerPoint PPT Presentation
Transcript of Experiment with an Auction to create a Demand Function
Experiment with an Auction
to create a Demand Function
Berufsakademie Eisenach Staatliche Studienakademie
Thüringen University of Cooperative Education
Prof. Dr. Stephan Rometsch
Demand Function
0 2 4 6 8 10 12 140
2
4
6
8
10
12
quantity
price
EXPERIMENT
Auctions and the Theory of Demand
PART I • Second price closed seal bid auction
• English auction
• First price closed seal bid auction
• Dutch auction
PART II • Demand Function and implications
Second price closed seal bid auction
ASSUMPTIONS AND INTRODUCTION
A bidder knows not the bid of others
Person with the highest bid gets the item
But he/she pays the price of the second highest bid
Why is it sensefull to reveal the true willingness to pay?
Simple: Because there is no regret!
Every other decision doesn´t gain any advantage!
I want to know Your true willingness to pay!
Therefore, I want to know Your true evalution of the good to create Your true
demand function
The true willingness to pay for the item of person i is zi
Background ?
Example
A person i evaluates the item with € 25,- (zi=25)
zi = 25gj = 20 gi =p =
cs = 5
If person i bids gi=zi and no one bids more – then he/she gets the item and has to pay p=gj=20, the
price of the second highest bid (of person j) and i gets a consumer surplus of 5.
Well ?1.
Would person i better off if he does anything else?
The result is the same. He gets the item and has to pay
p=gj =20, the price of the second highest bid and gets a true
consumer surplus of 5. Therefore, gi=zi=25 was high enough.
zi = 25gj = 20 ĝi = 28p =
cs = 5
Well ?2.
Would person i better off if he reduces the bid?
The result is the same. He gets the item and has to pay
p=gj=20, the price of the second highest bid and gets a true
consumer surplus of 5. Therefore, gi=zi=25 was ok.
zi = 25gj = 20 ği = 23p =
cs = 5
gi = zi = 25 was high enough
But…
Be careful, if gi<gj, then person j gets the item…
Now person j gets the item and has to pay p=gk=18, the
price of the second highest bid (of person k) and person i
is very angry.
zi = 25gj = 20ği = 17
gk = 18p =
Person i is very angry, because he wants to have the item, because his true willingness to pay was zi=25.
ResultsIf person i has the highest evaluation
To higher the price over zi doesn´t gain any advantage.
To lower the price under zi doesn´t gain any advantage.
If you lower the price, be careful, there is an increasing probability that another person j with the
bid gj has the highest bid and gets the item.
And then person i is very angry, because he wants to have the item, because his
true willingness to pay was zi=25.
Results
Therefore, reveal your true willingness to pay with your true bid and you get the item
for the price p, which is not higher then zi and you realize some positive
consumer surplus.
Note: The probability that the price p equals your bid gi and your willingness to pay zi is
close to zero:
probability (p = gj = gi = zi ) = 0
Another person has a higher bid 1. zj = gj = 28
Would person i better off if he bids ĝi=30 and not gi=zi =25?
Person i gets the item and has to pay a price which is higher
than his true willingness to pay zi=25 < p=gj=28.
Then he gets the item…. --- But, why ?
zi = 25 gj = 28 ĝi = 30p =
cs = -3
Another person gets the item 2. zj = gj = 28
Would person i better off if he does not bid gi=zi=25?
Person i doesn´t get the item and person j has to pay
a higher price as before p=ĝi=27 < gj=28.
Reduced cs for j – but what is the advantage for person i?
zi = 25 gj = 28ĝi = 27p =
Another person gets the item 3. zj = gj = 28
Would person i better off if he bids ği<zi and not gi=zi=25?
Person i doesn´t get the item and person j has to pay
a lower price as before p=ği=21 < zi=25 < gj=28.
Persons i and j are friends? – Again: what is the
advantage for i?
zi = 25 gj = 28ği = 21p =
large cs for j
Another person gets the item
If your bid is higher than your true willingness to pay, there is an increasing probability
that you get the item for the price p, which is higher then zi and you have to
pay more than your true evaluation and you realize some negative consumer surplus.
If another guy gets the item, then he has to pay the price of the second highest bid.
Be careful and don´t try to influence the price of others!
Don´t try to influence the consumer surplus of others!
Second price auction is equal to an ”English auction”
The auctioneer starts with a reserve price and bidders successively offer higher prices -
bids. Each bid exceed the previous by some minimal bid increment.
When no participant is willing to increase the bid further, then the item is awarded to
the highest bidder.
Normally the auction stops below the willingness to pay of the highest bidder.
Therefore, he pays the second highest bid!
Result is the same1.
Would person i better off if he does anything else?
The result is the same. He gets the item and has to pay
p=gi=20, the price of the second highest bid and gets a true
consumer surplus of 5. Therefore, gi=zi=25 was high enough.
zi = 25gjgi p =
cs = 5
12 15
gi gigj
17 2018
First price auction is equal to an ”Dutch auction”
The auctioneer starts with a high price and lowers the price successively until the first bidder
rises his finger.
When no participant rises his finger he reduces the price more and more.
The auction stops until the first bidder shouts:
“ Mine! ”
Then he pays the price were the auction stops, when he rises his
finger.
This is the first price!
Another Result 1.
The auctioneer begins with highest price, say 100.
Person i gets the item and has to pay his bid!
p = 60 = zi
zip =
60 70 80 10090
„MINE !“
60
What´s the problem for person i ? 1.
The auctioneer begins with highest price, say 100.
Person i gets the item and has to pay his bid!
But: What is in between the gap to the next highest bid?
Person i wants to wait until the auctioneer achieves a border
zip =
60 70 80 1009040
gj
BID
0
1
2,5
3
5
6
7,5
9
10
12
14
15
# BIDS
2
3
1
2
2
1
1
2
3
1
2
1
first idea: average price = 7,08
second proposal: p = 10 and 3 customers
Create the data
BID
0
1
2,5
3
5
6
7,5
9
10
12
14
15
# BIDS
2
3
1
2
2
1
1
2
3
1
2
1
QUANTITY
4
3
1
QUANTITY
21
19
16
15
13
11
10
9
7
4
3
1
QUANTITYQUANTITY
3
1
QUANTITY
1
Create the data
BID
0
1
2,5
3
5
6
7,5
9
10
12
14
15
# BIDS
2
3
1
2
2
1
1
2
3
1
2
1
QUANTITY
21
19
16
15
13
11
10
9
7
4
3
1
REVENUE
0
19
40
45
65
66
75
81
70
48
42
15
Create the data
BID
0
1
2,5
3
5
6
7,5
9
10
12
14
15
# BIDS
2
3
1
2
2
1
1
2
3
1
2
1
QUANTITY
21
19
16
15
13
11
10
9
7
4
3
1
REVENUE
0
19
40
45
65
66
75
81
70
48
42
15
Create the data
BID
0
1
2,5
3
5
6
7,5
p = 9
10
12
14
15
# BIDS
2
3
1
2
2
1
1
2
3
1
2
1
QUAN.
21
19
16
15
13
11
10
9
7
4
3
1
REV.
0
19
40
45
65
66
75
81
70
48
42
15
0 5 10 15 200
2
4
6
8
10
12
14
16
quantity
price
estimation:
p(q) = 15 - ¾ q
R = p*q = 9*9 = 81
y = -0,7863x + 15,536
R² = 0,9857
REV.
0
19
40
45
65
66
75
81
70
48
42
15
0 5 10 15 20
-10
0
10
20
30
40
50
60
70
80
90
f(x) = − 0.635199669982683 x² + 12.6080606553327 x + 8.4450309883674R² = 0.945545512412993
q
R
REVENUE
0 5 10 15 20 250
2
4
6
8
10
12
14
16
quantity
price
consumers surplus
= zi – p
1 1 1
6
5 5
0 0
3
p=9
q=9
R = p * q = 81
= (15-9) + 2(14-9) + (12-9) + 3(10-9) + 2(9-9) = 22
profit = revenue - costs
BID
0
1
2,5
3
5
6
7,5
9
p = 10
12
14
15
costs per unit: c = 6
price ↑ p = 10
quantity ↓ q = 7
revenue ↓ r = 70
profit ↓ π = 28
q
21
19
16
15
13
11
10
9
7
4
3
1
r
0
19
40
45
65
66
75
81
70
48
42
15
c
126
114
96
90
78
66
60
54
42
24
18
6
- 126
- 95
- 56
- 45
- 13
0
15
27
28
24
24
9
0 5 10 15 20
-100
-50
0
50
100
150
q
costs
revenue
profit
profit = 70 - 42 = 28
70
28
42
28
q = 7
profit = revenue + subsidy
BID
0
1
2,5
3
p=5
6
7,5
9
10
12
14
15
q
21
19
16
15
13
11
10
9
7
4
3
1
r
0
19
40
45
65
66
75
81
70
48
42
15
s
- 147
- 133
- 112
- 105
- 91
- 77
- 70
- 63
- 49
- 28
- 21
- 7
147
152
152
150
156
143
145
144
119
76
63
22
Subsidy per unit s = 7
price ↓ p = 5
quantity ↑ q = 13
revenue ↓ r = 65
profit ↑ π = 156
But: price is not zero!
Additional costs per unit or subsidy
influences the marginal behaviour.
0 5 10 15 20
-200
-150
-100
-50
0
50
100
150
200
q
profit
subsidy
revenue
q=13
156
65
quantity increasing: q =13price reducing: p = 5
T-shirt as a present for every participant –
logical equivalent to the total price discriminating monopolist.
consumers surplus =
0 5 10 15 20 250
2
4
6
8
10
12
14
16
quantity
price
p = 0
zi – p = (15-0) + 2(14-0) + … + 2(0-0) = 138
= monopolistic profit
Compare Theory vs. Experiment I
1. Demand
EXP: q = 9
bqaqp q43
15p
qbqaqqpqR qq43
15R
²bqaq ²q43
q15
02bqaR´ 0q2
315R´
2b
aq 10q
2. Revenue
3. Marginal Revenue
! !
Compare Theory vs. Experiment II
EXP: p = 9
b2a
bapbqap
2a
*p
q43
15p
5,7*p
cqqC q6C
cqqbqaq
0cbq2a´
q6qq43
15
06q23
15´
4. Price
5. Costs
6. Profit maximization
! !
Compare Theory vs. Experiment III
EXP: p = 10
EXP: q = 7
EXP: π = 28
b2ca
q
2
cap
6
5,1615
q
cqqbqaq 666643
156q
π
276q π
7. Quantity and Price
8. Profit
10,50643
15p
Literatur
H. VARIAN, Intermediate Microeconomics - A modern Approach, Norton, Chapter 17: Auctions
A. ROTT, Die Nachfragefunktion: Ein ökonomisches Experiment für die Lehre, Dortmunder Diskussionsbeiträge zur Wirtschaftspolitik, Nr. 92, Juli 1999
T. Bergstrom, J. Miller, Experiments with Economic Principles, McGraw-Hill, 1998. (http://zia.hss.cmu.edu/miller/eep/eep.html)
Thank you for attention!
Vielen Dank für Ihre Aufmerksamkeit
Prof. Dr. Stephan M. Rometsch
Berufsakademie Eisenach Staatliche Studienakademie Thüringen
