Deentralized Trade Imagine barriers between you and other buyers or sellers: legal, spatial, soial, or temporal These barriers redue the set of goods you an trade, and this redues welfare in some sense One extreme is autarky : a good or servie is illegal to trade (e.g.,organs) The other extreme is a ommonly traded ommodity: you an buy as muh as you want without any hassle (e.g., medium-sized navy blue tee-shirts) Today we want to disuss the in-between ases: how do barriers between buyers and sellers lead to welfare losses? A Simple Market I ve handed out ards to everyone If your ard is red, you are a buyer, and the fae value is your value for a good, v If your ard is blak, you are a seller, and the fae value is the ost of your good, We ll divide the lass up into different groups, and within the groups you must reveal your ards to potential trading partners (no adverse seletion) If a buyer and seller trade at a prie of t, the buyer s payoff is v t and the seller s payoff is t Soial planner/perfetly ompetitive equilibrium There are 40 ards (ae to 0), 20 red and 20 blak If we want to maximize the gains from trade, we take the buyers with the highest values and math them with the sellers with the lowest osts; the seond-highest values with the seond-lowest osts; and so on, until we reah v = 5 and = 5 So the effiient quantity of trade is 0 at a prie of 5 Autarky You are alone. Trade. OK, not very interesting...
Bilateral trade Break up into pairs within your rows, going from left to right. You have 2 minutes to negotiate. How many pairs traded? At what pries? Row-lateral trade Now, anyone within a row an trade. You have 5 minutes to negotiate. How many pairs traded in eah row? At what pries? Class-wide trade Now, anyone an trade. You have 2 minutes to negotiate. How many pairs traded? At what pries? Tightness Market tightness is the ratio of buyers to sellers or vie versa: the number of agents on the large side of the market divided by the number of agents on the small side What if we have all the buyers in the lass trade with one randomly seleted seller? How many trades at what prie? What if we have all the sellers in the lass trade with one randomly seleted seller? How many trades at what prie? How does tightness matter to outomes? Model There are i =, 2,..., I buyers and j =, 2,..., J sellers, where I > J. Households take the prie p as given and hoose a quantity q to solve max log(q) pq + w, q while sellers take prie as given and hoose a quantity to solve max pq q 2 q2. Centralized market: all I buyers and J sellers trade at the same time, at the same prie Deentralized market: eah buyer i has a probability J/I of being mathed to a seller j, and then i and j engage in bilateral trade 2
Centralized Trade Eah household i has demand q i (p) = p, so total demand is Eah firm j has supply so total supply is Q D = Q S = I q i (p) = I p i= q j (p) = p, J j= q j (p) = Jp Centralized Trade Imposing market learing implies that Q D = Q S, or I Jpen I IJ = p en = pen J, qen = If we define market tightness as I/J, the prie is inreasing in tightness and the ost parameter Deentralized Trade If eah buyer and seller bargain bilaterally, their individual markets lear when q i (p d ) = q j (p d ), or p = p p =, q = So the prie in the deentralized market is p de =, and the quantity traded is q de = Jq = J/. Deentralized Trade The quantity traded in the entralized market is higher, beause IJ JJ q = > = J = q d, and the prie is higher, beause p = I J > 3 J J = = p d
Higher quantity and higher prie? In the entralized market, a given household is getting less quantity than a household in the deentralized market, so that it has a higher marginal benefit and pries are higher; but more people are trading in the deentralized market, so the quantity is also higher. Centralized vs Deentralized Trade Welfare In the entralized market, the soial planner is solving max q D,...,qD I,qS,...,qS J subjet to I i= qd i = J j= qs j I v(qi D ) i= J C(qj S ) But the deentralized market adds set of onstraints: only, say, the first J buyers an trade with the J sellers, so that for k =, 2,..., J, qi D = qj S The optimum for the less onstrained problem must be higher, so the entralized market must have higher welfare Searh and Missing Markets A market has searh fritions or ineffiienies from deentralization if agents trade the same good at different pries in different times or plaes, resulting in ineffiieny relative to a entralized market. j= 4
If searh beomes infinitely ostly, so that no trades our, the market is missing. Examples from finane: there are regional trading exhanges that the FTC is onsidering integrating; banking servies in the US used to be state-bystate; assets whose returns have negative ovariane offer hedging value, regardless of whether the goods are related in any sense Examples from e-ommere: Uber and abs; Upwork and programmers and graphi designers and et; Etsy and handrafted goods Searh Markets versus Missing Markets: Solutions Government intervention: reate new markets, allow trade integration in existing ones (e.g. 9th entury banking onsolidation) Soial entrepreneurs: reate new tehnology/markets to allow trade to happen more effiiently, harge an entry or transations fee 5