Tutorial 1: An Allocation Problem
Matthew Robson
Trade Game
-Everyone has a card with a role, Buyer or Seller, and a reservation
price
-Your reservation price is for some hypothetical good
-If you are a buyer, this is the maximum price you are willing to pay
for a good
-If you are a seller, this is the minimum price you are willing to sell
your good for
-You must try to trade with others in the room, ie the buyers buy from
the sellers, and the sellers sell to the buyers. So you can make profits.
-For buyers you make profit if you pay less than your reservation price
-For sellers you make profit if you sell for more than your reservation
price
1
Trade No.
Trade Price
Reservation Price
Buyer
Seller
Profit
Buyer
Seller
1
2
3
4
5
6
7
8
9
10
2
3
4
5
(1) Who buys and sells at each price?
How many goods are exchanged? What is the surplus each group
receives?
What is the competitive equilibrium?
Some people will get zero, is this fair?
Assumptions
1. A seller who is indifferent always sells and a buyer who is indifferent always buys.
2. If there is rationing, the good is allocated in order to maximise the surplus.
6
Price = £18
Trades = 1
Seller Surplus = 7
Buyer Surplus = 0
Total Surplus = 7
7
Trades = 2
Price = £17
Seller Surplus = 11
Buyer Surplus = 1
Total Surplus = 12
8
Trades = 3
Price = £16
Seller Surplus = 12
Buyer Surplus = 3
Total Surplus = 15
9
Trades = 4
Price = £15
Seller Surplus = 10
Buyer Surplus = 6
Total Surplus = 16
10
Trades = 4
Seller Surplus = 6
Price = £14
Buyer Surplus = 10
Total Surplus = 16
11
Trades = 3
Seller Surplus = 3
Buyer Surplus = 12
Price = £13
Total Surplus = 15
12
Trades = 2
Seller Surplus = 1
Buyer Surplus = 11
Price = £12
Total Surplus = 12
13
Trades = 1
Seller Surplus = 0
Buyer Surplus = 7
Total Surplus = 7
Price = £11
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(2) Now suppose all the sellers group together.
They form a cooperative and choose a single price to sell their
goods.
What is their chosen price?
At this price, what are the surpluses – individual and aggregate?
Is this better than the first scheme? Is it fairer?
(3) What would happen if the buyers grouped together, to form a
cooperative?
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Seller Optimal 
Buyer Optimal 
Price
Trades
£18
Surplus
Seller
Buyer
Total
1
7
0
7
£17
2
11
1
12
£16
3
12
3
15
£15
4
10
6
16
£14
4
6
10
16
£13
3
3
12
15
£12
2
1
11
12
£11
1
0
7
7
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(4) What might happen if both groups form cooperatives?
(5) Are there any other Exchange Mechanisms you can think of ?
-Is there a mechanism which maximises the number of
exchanges?
-What are it’s properties?
17
Price 1 = £18
Price 2 = £17
Price 3 = £16
Price 4 = £15
Price 5 = £14
Price 6 = £13
Price 7 = £12
Price 8 = £11
Seller Surplus = 0
Buyer Surplus = 0
Total Surplus = 0
No. of Trades = 8
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(6) Is the total surplus always maximised in a competitive
exchange?
Is the total surplus in the competitive always (strictly?) greater
than this under monopoly or monopsony?
Is it always the case that there are some buyers who cannot buy
and some sellers who cannot sell under any form of exchange?
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