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 Profit Buyer Seller 1 2 3 4 5   2 3 4 5 6 7 8 9 10 Record all trades in this table, then run through it. 2

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Who buys and sells at each price? (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

Trades = 1 Price = £18 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 Seller Surplus = 10 Price = £15 Buyer Surplus = 6 Total Surplus = 16 Price = £15 10

Trades = 4 Seller Surplus = 6 Buyer Surplus = 10 Total Surplus = 16 Price = £14 11

Trades = 3 Seller Surplus = 3 Buyer Surplus = 12 Total Surplus = 15 Price = £13 12

Trades = 2 Seller Surplus = 1 Buyer Surplus = 11 Total Surplus = 12 Price = £12 13

Trades = 1 Seller Surplus = 0 Buyer Surplus = 7 Total Surplus = 7 Price = £11 14

Now suppose all the sellers group together. (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? What would happen if the buyers grouped together, to form a cooperative? (3) 15

Price Trades Surplus Seller Buyer Total £18 1 7 £17 2 11 12 £16 3 15 £17 2 11 12 £16 3 15 £15 4 10 6 16 £14 £13 £12 £11 Seller Optimal  Buyer Optimal  16

What might happen if both groups form cooperatives? 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? (4) (5) (4) Meet somewhere in the middle. Fail to trade at all. (5) Monopoly, Monopsony, Oligopoly, Oligopsony, Monopolistic Trade mechanism on following page… 17

Price 1 = £18 Price 2 = £17 Price 3 = £16 Seller Surplus = 0 Buyer Surplus = 0 Total Surplus = 0 No. of Trades = 8 Price 4 = £15 Price 5 = £14 Price 6 = £13 Price 7 = £12 Price 8 = £11 Maximise the number of trades, but no one makes any surplus. Is this fair? Efficient? 18

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? (6) (6) Yes, see table. Yes, see table. Yes, preferences of goods. 19