Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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# The Macroeconomics of Supply Chain Disruptions

Authors:   
Discussant: None  
Video: https://www.youtube.com/watch?v=zLXIyBTD8oA&t=0s


## Talk (00:00:00 – 00:27:32)

[00:00:00] um thank you let me run my timer so that I can okay perfect so um thanks a lot U for um putting this paper on the program um so the motivation of the paper is sort of very similar to what Matt started talking about you know if you  
[00:00:14] want to think about um produ production any mod modern industrialized economies you can really think of it as a complex network of Supply chains you know just to put some numbers on it this paper bar not at all they document that you know in small country like Belgium the median  
[00:00:28] firm relies on50 3 suppliers and 26 customers and you know this can become much more stew for much larger firms like airb at least Airbus claims that they work with 12,000 different suppliers of pro uh that provide  
[00:00:41] different parts and services now you may want to ask why do firms deal you know essentially locate themselves in Supply chains why don't they produce the goods themselves and you know the idea is sort of trivial and goes back maybe can argue  
[00:00:54] to Adam Smith you know Supply chains allow for better specialization a final division of labor and you know eventually increasing productivity just you know as an example you know just to keep in mind you know I guess presumably  
[00:01:07] Airbus can produce its engines inh housee but probably it's much more efficient if they Outsource it to GE or rollsroyce and they you know they produce those goods now and the idea is that you know firms when they do this specialization and they they produce  
[00:01:22] different parts but then they have to maintain this relationship so that the engine that he is producing can be actually implemented on air buses on airbus's um airplanes you know so for example just to give an idea um you know  
[00:01:35] Teresa Fort documents that you know many manufacturing FMS rely on customized Outsourcing in the sense that um Airbus plus GE I want this this Engine with this characteristics and they maintain a relationship in order for these input  
[00:01:49] products to be able to be combined together turning into turning into an now if you buy this story there's a flip side to it which again Matt mentioned and that is that when the supply chain supplyer customer relationships are  
[00:02:01] dissolved or are disrupted then they actually destroy relationship specific Surplus that the productivity that's that's you know encoded in that relationship may actually get damaged and presumably they can have  
[00:02:14] macroeconomic consequences so you know some of the more recent examples you can think of natural disasters the covid pandemic to some extent the Russian invasion of Ukraine you know and these are more than anecdotes in the sense that at least policy makers seem to be  
[00:02:28] concerned about these these issue so you know going back to 2012 this is a document called the US natural strategy for Global Supply CH security put out by the Obama White House and you know I just quote that they say integrated  
[00:02:41] Supply CHS are fast and cost efficient but also susceptible to shock that can rapidly escalate from localized events into broader disruption so they add supply chain relationships they they you know they are a source of productivity  
[00:02:55] and specialization but then the flips out of that when they're when they're disrupted they can have negative consequences not just for the firms but also uh for the broader macroeconomy so what do we do this in this paper this is  
[00:03:07] going to be a theoretical paper to allow us to think about uh macroeconomic consequences of disruption to supply chain but before I G give you the the model and consequen I want to make an argument that if you want to you know  
[00:03:21] study the macroeconomic consequence ofly theoretically in a systematic way you need a model that has uh at least three three ingredients one is firm specific relationships that contribute to productivity so this is exactly the  
[00:03:34] example of GE and and and uh and Airbus or or any of the other customiz supplies of Airbus the is that there is you know the the Airbus and G you know airb doesn't go to the market to the bazaar  
[00:03:48] and buy shop or engines they actually these these engines are designed for particular aircraft and they there is this specificity to this relationship number two is that once you buy the argument that these relationships specific whatever model you write cannot  
[00:04:01] be competitive Airbus and G are not price takers they are not dealing with a large set of other other firms and then finally whatever model you write it has to have a non-trivial extensive margin of adjustment at the  
[00:04:15] end the day if you're interested in Supply chains instru you want to have a model in which you know this relationships can break down or can be formed based on you know F Technologies and per so that's exactly what we do in this paper we try to write down a  
[00:04:28] hopefully model that bring all these three ingredients into a single framework so just to repeat the model is going to have uh the productivity in this model is going to be captured encoded in the supply customer relationships the relationship are  
[00:04:43] customized for the two firms that are at the two end firms are going to decide who they form links with where so as a firm I decide who my suppliers are who my customers are so if you can think of this this is going to be essentially a  
[00:04:56] model of net information and finally we're going to assume that is going to split the any surplus they generate bya bargaining so this is not going to be a competitive model this is the departure from the competitive framework langage so what do we get well first I have to  
[00:05:10] you know walk you very quickly over some like basic results that make this framework usable so I have to talk about existence and uniqueness of equilibria I'm going to give you some close form characterization results then I'm going to give you some compartive static results basically thinking about oh if I  
[00:05:24] have a disruption here how would it impact the distribution of cellplus throughout the economy how would it change terms incentives to form or dissolve relationships with suppliers or customers and then I'm going to zoom out and talk about macro outcomes and then I'm going to talk about what I think is  
[00:05:39] most more important is thinking about the model's implications for efficiency and fragility so rather than going through the text maybe it's easiest if I show our main result via picture here so  
[00:05:51] think about here on the xaxis this is some negative shock to the to the economy you can think of like there is a reduction in productivity some terms productivity or it can be some increase in some form of cost so and then here on  
[00:06:05] the Y AIS I have AG out to their GDP and first look at the blue curve the blue curve is the aggregate output when under a social planners problem so essentially an efficiency Benchmark and as you can see as the shock increases essentially  
[00:06:20] the planet cannot produce as much as before and output goes down okay and there may be some Kinks but it goes down continuously so the first result I'm going to get eventually hopefully I have time to get to it is that the red curve which is the same thing for equilibrium  
[00:06:33] is below the blue curve this basically shows you that the model I'm going to present to you is inefficient so there would be some externalities in this model in half firm form relationships they don't do it efficiently and second  
[00:06:46] not only the red curve is below the blue curve there are these discontinuities in the red curve that do not exist in and this these are you can think of these as sources of fragility so when there are small shocks to this economy you know  
[00:06:59] maybe the cost some cost goes up by a little bit you may actually get very large discontinuity in the GDP in the economy essentially the econom would be impacted very severely at the m so sort of if you want to get take a this would be sort of the mental picture that comes  
[00:07:14] out out of the mod which you know hopefully I'll get all right and then we're going to have some other results which are consequences of of these inefficiency of fragility is that you're going to have a productivity fragility trade off essentially you know you can  
[00:07:27] think about an economy FS decide to have more fragmented Supply chains you're going to have more stages of production and that would enhance productivity but it may come at the cost of higher fragility so then in most of the times you're doing well but in bad times the  
[00:07:41] economy may may actually suffer the another prediction of the model the supply CHS are going to be procyclical in the sense that in good time firms are going to invest more in building relationship and then these unad times in when shocks are realized can start  
[00:07:56] dropping this relation and finally I'm going to show you that the mod is going to capture a nonlinear amplification mechanism and sort of the big picture idea is that you know small shocks of Supply chains may not actually Amplified a lot but it's the large shocks that are  
[00:08:09] going to be Amplified the Corel to this statement is that you know maybe in standard uh time you don't need to worry about uh and in during normal recessions you don't need to worry about um disruption and it's only like during  
[00:08:23] severe recessions theing disrup is become all right so let me skip the the literature review and get to the model as I said this is going to be a non-competitive model of relationship specific Supply chains so the model is going to have n plus one F and firms one  
[00:08:37] through n are going to produce different intermediate goods and they're going there's going to be a firm zero that produces a p we're going to borrow this mechan this uh framework from paper a Learners are in which firm I has access  
[00:08:51] not just to one production technology by a host of different production technology so think about this fi this is the production function of firm I and index by different set of inputs I I that the firm uses so I can produce an  
[00:09:04] aircraft with a G engine or I can do it with a r Source engine you can treat this as potentially two different Technologies that's available to B and each one of those Technologies would have its own productivity and then to produce obviously you have to use uh  
[00:09:17] labor and you have to buy intermediate input obviously you buy the intermediate input from the suppliers of that technology okay so each as a firm you can imagine you have access to many different Production Technologies now this is where we're going to depart  
[00:09:31] from the AAR paper and the idea we're going to make is the following assumption that for a firm to use a particular mix of intermediate input The Firm has to establish customized customer Supply relationship with each one of those suppliers so  
[00:09:45] again if I'm if I'm airbo and I want to use G I have to form a relationship with that F like you know I have to set up my production plans and I have to design my aircraft such that that that that you know that that engine would fit with the rest of them and the and at the other  
[00:09:59] side GE has to do the thing okay so formally we're going to model this the F way that you know if firm J want want to be a supplier to firm I both parties have to pay fixed cost the customer pays a fixed cost C and the supplier pays a  
[00:10:13] cost SI once we pay theix cost we form a relationship the key assumption that we're going to need in this model for this for everything I'm going to tell you to be uh to go through is that these costs are relationship specific so when  
[00:10:27] I form a Rel with the cost app to uh to form a relationship with a firm it cannot be transformed and translated to another firm and then these costs are s so examples would be you know you can customize your product you have to integrate your production process with  
[00:10:42] the other party the two firms have to do joint R&D Investments that you know it's very specific to that relationship and so on and so so once these form uh for pay the cost and form the relationship essentually going to be left with a firm  
[00:10:54] level network of so that's the production side of the economy the household size is going to be very boring there's going to be representative household that provide L units of Labor in El last to the firms and FES the following budget con so my consumption is going to be equal to the  
[00:11:09] wage uh wage income plus any profits uh the hustle gets from the firm and the net profit I The Firm gets from firm I the household gets from firm I is going to be the gross profits of the firm  
[00:11:21] minus whatever cost the firm has to F pay to form relationships okay so this just essentially the household budget constraint there's a technical assumption that I ski so this is going to be the timing of the model so it's equal to zero as I mentioned each firm  
[00:11:36] in the economy decides to pay fixed cost to form relationships to serve as a supplier and customer to any potentially any other firm in the economy and if both parties pay the cost then you end up with the production Network which I'm going to show with G now once then at  
[00:11:50] equal to one any two firms that have a relationship they have to negotiate over a pairwise contract and if the two firms agree to the contract then they can trade it equal to I haven't told you ex yet how the contract are formed but once  
[00:12:03] the two firms form a contract write a contract then thatal to two basically it's when firms make input output decision and the households make their consumption okay so the last thing I have to tell you about the model is essentially how do what what type of  
[00:12:17] contract so we're going to assume that FMS are going to write two part tariffs in the following sense if firm I and J get together they're going to write a contract which has two components one is a per unit price so imagine Chad is my  
[00:12:31] supplier and he promises to deliver as many units as I demand at this fixed price P but then in in in exchange I'm going to pay him an up upfront lumpsum transfer ti so I pay him this this transfer and then he makes this  
[00:12:44] commitment and we're going to assume that these prices and transfers can be contingent on the set of relationship in the cont okay and now given this you can basically write down the firm's uh profit so the net profit remember is the gross profit minus whatever cost cost  
[00:12:59] you pay to form relationships but then the gross profits of per I is my sales to any customer minus whatever expenditure I have on my intermediate inputs minus any expenditure I have on  
[00:13:11] on on labor inputs then I make this trans then I get these transfers from my customers but then I have to make these transfers to my potential suppliers so this would be firm's gross profit okay and these are the contract and now this is where the non-competitive part comes  
[00:13:25] in we're going to assume that firms are going to do Nash bargaining over these contracts so basically the the contract that Chad and I agree to is going to be the outcome of KN bargain between Chad and I where Theta I is the bargain power of firm I and Theta J is going to be the  
[00:13:40] bargain power of firm J okay so we're going to just assume standard all right so just summarize T equals to zero firms they cost form relationship T equals to one firms that have a relationship they bargain over these two part par contracts equal to  
[00:13:55] two if they agree is when production and consumption take okay so now to analyze the model I'm going to start at t equal to 1 and two but now ignore t equal to Z ENT I'm going to take the network she Exogen and then I'm going to go back  
[00:14:08] toal to zero and analyze it so first let's look at exogenous production to do this I'm going to Define two concepts that are going to be crucial first I'm going to define the aggregate productivity given a production Network  
[00:14:21] G is the maximum amount of the final good the economy can produce per unit of Labor so you can think of this Agri productivity the object as parameters in the production possibility Frontier so if Network G1 is a subset of G2 there  
[00:14:34] are fewer relationships then obviously you can produce fewer Goods you know this is a statement about essentially the the frontier the production and I'm going to say network is feasible if the total cost of forming  
[00:14:48] the relationships is less than the total output that those relation can generate essentially saying that the cost fall inside the production possibility Okay so now this is the first result just to get me started so  
[00:15:01] it says that if the network is feasible and equilibrium exists and it's generically Unique and um and all Supply customer relationships are for all Supply customer relationships uh reach an agreement also customer pairs  
[00:15:15] within that g reach an agreement with the bar now let me get to the characterization so the first part of this theorem says that all intermediate input producers are going to price the marginal cost essenti they're not going to be any markups the reason is that  
[00:15:29] when Chad and I bargain we bargain over by assumption or bargain over these two-part tarff contract which means that what is going to maximize the size of the Surplus between the two of us is that Chad is going to price a marginal cost and then extract any surplus he  
[00:15:43] wants from me via those Trends that's why firms are going to have marginal cost price now what are those transfers well those transfers are going to be such that firm any firm I profit even a particular production network is going to be given by these Expressions so for  
[00:15:57] those of you who remember your 1950 Game Theory this is just a variation of taply value but for those of you who don't this is actually sort of very intuitive object it basically says the expression in red here is the marginal contribution  
[00:16:11] of firm I to aggregate productivity when I look at a subset of firms key so this is aggre productivity when when the set of active firms is key without I and I firm add firm I this is by how much agre productivity goes off so this is essentially marginal contribution for  
[00:16:26] agre productivity and then I'm going to have have a dated out of this uh margin of contrib AG productivity where the weights are given by firm bargaining poers okay so this is sort of a characterization of firm profits because  
[00:16:39] this is a little bit of a maybe unfamiliar expression let me go through a very quick example to give you a s imagine this very simple economy in which firm zero and one are the two present firms for now ignore firm two well this result reduces to the  
[00:16:53] following standard uh what you would expect the firm zero is going to firm the two firms are going to split the total Surplus that they generate together proportionally to the now let me add term two to this economy now the  
[00:17:07] same expression of TR value expression I show you is going to do the following says the firm want's profit is be whatever it had before plus this new blue term what is this new blue term well it's easy to sort of get a sense of what it does imagine this FM two is  
[00:17:21] completely useless in the sense that it adds nothing to agre productivity in this case this firm this term is going to be zero exactly as if firm two is not there if firm two produces good that's substitute to firm one then this glut is  
[00:17:35] going to be negative essentially FM two is going to steal some business from firm one as you would expect because FM one has a competitive and now if this G2 is is a compliment to good one then that's going to increase uh then that's going to increase uh the profit of okay  
[00:17:50] so with that said now let me get to efficiency so now remember I'm still assuming that the production network is exogenous then given this exogenous production Network the equilibrium is going to be efficient and this is just the consequence of the fact that f price  
[00:18:05] Mar cost so the implication of this is that any inefficiency I'm going to result I'm going to show you now is going to come from the fact that Supply customer relationships are inging all right so now let me skip the comparative static results because I'm running low  
[00:18:19] on time but let me just Define one one give you one assumption that I would need I'm going to say if I have two production that was G1 and G2 I'm going to say the productivity super modular if  
[00:18:31] I add a relationship to firm G2 it to to network G2 it's going to raise aggre productivity by more than if I add it to to to to G1 okay so this is just what I mean by super modularity and you can  
[00:18:43] have an intensive margin equival version of that as okay so let me skip this compartive Statics and get to what are most more interesed in how firms actually form relationships so here is a  
[00:18:56] result it says if if AG productivity is super modular then an endogenous Network equilibrium exists even though their equilibrium is not unique there always exist the greatest equilibrium G star that contains all of their equilibria  
[00:19:10] some sub networks and that aggregate output and all firms profits are going to be highest in this G Star so from now on I'm going to look at this G Star because it's as if it's this is the equilibrium that that has no  
[00:19:23] coordination now this result says that this is the consequence of the previous one is that if once you have this super modularity and you increase any of these fixed cost of forming relationship that's going to shrink the set of supp customer relationships that are active  
[00:19:37] in equilibrial it's going to reduce offer profit and it's going to reduce aggregate out same thing if you reduce any of the payse productivities firms are going to drop their supply customer linkages they're going to Red the their net  
[00:19:52] profits are going to go down and aggregate outut is going to fall okay so this is the sense in which I mentioned earlier the supply customer relationships are going to be procyclical in down term the firms are going to shed the supply customer  
[00:20:05] relationship because they're no longer atable so now with that said let's get to the um to inefficiency and fragility results the theorem says if aggregate output is super modular then gar which  
[00:20:18] is the greatest equilibrium production network is going to be a subset of what a planner would have done if the planner could choose all relationships a different way of saying the statement is that firm under invest in this model in  
[00:20:30] their supply customer relationship to understand the the economics of this it it's better to think about two there are really two economic mechanisms underpinning this this this inefficiency  
[00:20:43] so think about adding a relationship I to a network G when you add a new relationship to the economy it's going to change band profits bya two channel on the one hand obvious is going to expand the production possibility Frontier which means that you know firms  
[00:20:58] are going to be you know the the there is more resources to be produced and you know there is there is more soft in the economy and this is going to be shared among all firms but the firm inj who are paying the cost of firm in that relationship they're not going to be  
[00:21:11] able to appropriate all the Surplus that they generate so this essentially creates a positive externality on all other fs and it's a for and a force worth on their investment Chad and I make the investment it benefits not just  
[00:21:24] us but chat suppliers and my customers and the rest of the firms in the economy so that that becomes a force towards under investment the policymaker would have wanted us to invest more the other mechanism is that once we add a relationship this is actually going to  
[00:21:38] change the bargaining positions affirmed in this pairwise bargaining problem and it would have it would help I andj above and beyond what the planet would have want essentially this creates a negative business dealing externality and a force towards equilibrium over investment the  
[00:21:52] super modularity assumption that I imposed on this result ensures that the net exter ity is going to be positive essentially the Surplus expansion effect is going to dominate Surplus redistribution effect that's why there's going to be under investment in  
[00:22:06] equilibrium uh in this mod okay so that's inefficiency now I'm going to talk about fragility so let me call this y efficient and Y star to be aggregate output in the  
[00:22:21] efficient allocation and under the under equilibrium this result says the efficient allocation is going to be continuous in all the shocks whereas y star is going to be discontinuous this is sort of the result I showed you in the very first graph Espen an  
[00:22:35] interpretation of this is that equilibrium Supply chains are not only inefficient but also are excessively fragile because you're going to have these discontinuity a different way of saying this is that the fragility and efficiency are in this model are two  
[00:22:49] sides of the same con they're really one and the to give you the intuition for this result it's easy to think about a very simple example imagine have a pair ofs I andj and the only active Rel or the only relationship that um requires a  
[00:23:04] fixed cost is this relationship imagine everything else is either free or completely just not worth and let's think about what happens if I increase the fixed cost of this relationship in the efficient allocation well obviously as the cost of the relationship  
[00:23:17] increases as s goes to the right the social planner you know keeps this relationship but now has to spend more resources to keep this relationship going and obviously output is going to fall beyond the certain threshold here  
[00:23:31] then this relationship is no longer worth it so the planner drops the relationship and Beyond which if I increase the cost of that relationship well it has no effect on us but now let's think about what happens in equilibrium well remember in equilibrium  
[00:23:45] the firm is going to drop this relationship before the planner would have wanted the firm to do it that's the that's really the inefficiency in this model so what happens is that as I increase this s at some point from I from J is is going to drop this  
[00:23:58] relationship and I'm going to go down to the level that the planner would have gone to at a different point essentially firm J is going to D dropt this relationship at its indifference point but that's different from the planner's indifference point which is going to be here and that's really the source of the  
[00:24:13] inefficiency here okay and that's what gives you the inefficiency gives you this discontinuity so that's why I said inefficiency and fragility are two Ty of coin okay so I forgot how much time I  
[00:24:25] have uh Chad can help me one minute I guess um um so um so this is going to be uh minutes on the ra okay sounds great so I can get to at least one of the  
[00:24:37] applications here so imagine you have a very St the economy so I'm not showing the rest of the economy I'm just showing you two pairs pair of firms a pair of firms here and imagine this is a integrated vertically integrated  
[00:24:51] architecture and now imagine I consider an alternative architecture in which I have like a fragmented relationship so rather than firm is selling to firm i j is going to sell to K which is going to process it and give it to firm I and I'm going to just impose the assumption that  
[00:25:05] fragmentation increases agre productivity okay so this is something that's good it Rees efficient now this results says that there is going to be a threshold be below which the fragmented economy is  
[00:25:19] going to be better but beyond which the the integrated econom is going to be better what is the intuition for this result it's again easy to do it in a figure like this so let's start from here when the fixed costs are small well the fragmented economy is going to be  
[00:25:34] more productive than the integrated economy just by assumtion of fragmentation raises productivity because of specialization but remember both of these two economies are going to go through their own points of discontinuity and it's totally possible on second parametrization that the  
[00:25:49] fragmented economy is going to go through its discontinuity before the integrated economy so essentially not only even though you get a higher productivity here you're going to get a larger drop and an earlier drop in  
[00:26:02] response to shocks in the fragmented economy than in the integrated economy so this is what I mentioned in the beginning that you're going to face an A A trade-off between fragility and and and uh and uh and and  
[00:26:16] productivity um so got to have two more applications but it's because I don't have time I just mention them you can have like strong amplification mechanisms in this model and there's going to be a nonlinear amplification mechanism in the model by which I mean  
[00:26:30] that this is uh that uh uh there's going to be small shocks are not going to be Amplified by much in this economy but large shocks are going to be Amplified significantly or a different way of saying the same same St statement is that supply chain disruptions become  
[00:26:45] more relevant during severe downturn than you know just more your uh year-to-year uh fluctuation um so let me just stop here I presented the track of macro model of Supply chains in view it captures like three really important ingredients that  
[00:27:00] not all three show up in in in in a single model to the best of our knowledge firm specific relationships that contribute to productivity that which requires a departure from competitive framework and a non-trivial excessive margin of adjustment and the  
[00:27:13] model delivers we think this interesting result that you know there is inefficiency that exist in for relationships is really the core at the the fragility that that arrives in in supply chain and that leads to a productivity fragility tradeoff and a  
[00:27:27] linear application okay so let me stop here