Technical Efficiency, Allocative Efficiency and Economic Efficiency

[music] [music] Hi, welcome back to the course Applied Production Analysis Using MATLAB. In today's session, we'll be revisiting the concept of technical efficiency that we have already discussed in the last class, where for now we'll consider the two inputs, one output case. Also, we'll introduce a few more related concepts, especially from performance evaluation that is frontier-based performance evaluation. One is allocative efficiency and the other one is tech-economic efficiency, where these three concepts are interrelated. So from a very simple two inputs, one output case, as we have already discussed, you can conceptualize the production frontier or technology set by using the concept of isocost. So we'll be using an isocost framework. Say you have input one that is x1 here, input two x2 over here. So just to make our lives a bit easier, we'll try to make both inputs in density form, that for one unit of output how much input x1 and x2 are being used. With that, we'll be getting, we can conceptualize an isocost, say like, we name it as SSSash, and this isocost shows what is the level of or various combinations of x1 and x2 that needs to be disposed or used from a production point of view to produce one unit amount of single output that we are having, that is Y. So now coming back to our performance evaluation, the very first performance evaluation that we had was the technical efficiency. So now we need to see whether one observation, say operating at this point producing one unit of output, assume that way, whether it is technically efficient or not. So revisiting the same concept what we have already discussed in this context, it is more of an input approach where the firm is operating at this point, say P. We need to see how much extra input the firm uses for producing the level of output that is y, one unit, and what is the deviation or the level of inefficiency that it has from the frontier. So for that, we'll conceptualize a framework where we are trying to reduce the input usage of both input one and input two, that is x1 and x2. So we are trying to reduce both x1 and x2 at the same rate. So here it can be named as radial contraction. But in case, there can be a where you can reduce one input more proportionately than another input, that will be a non-radial contraction that you can consider. So here what we are doing, we are connecting the point P with a line passing through origin. So that gives us an idea how much the firm P or how much the decision-making unit that is operating at point P is deviating from the potential outcome. So here you can see we mark this point on this isocost Q. And here you can see OP is the actual combination of x1 and x2 or the intensities that firm is using. But if the firm was technically efficient or given the technology, the firm could have produced the same level of output by operating at point OQ, but it is operating at point OP. So that will give us a value less than 1. That means the firm operating at P is technically inefficient. And this ratio of OQ by OP will give you the level of inefficiency the firm is operating at. So here we can see it is somewhere half of the U distance. So in some sense, we can say that the firm can reduce the input intensities of x1 and x2 half, or it could have reduced its inputs half as compared to the actual level of operation that it is going through presently. So that shows the level of inefficiency or the potential reduction that the firm could have done. So now we approach the same problem but from a different perspective. Here what we are doing so far, what we discussed, it consists of only the actual amount of inputs being used for production purposes. One main problem is a missing component, that is the price or the cost of production. Since both x1 and x2 will involve price, say w1 and w2, we need to take into account the price of x1 and x2 into the picture and see given these prices how the firm is utilizing x1 and x2 for the production process. So to plug in the price into the picture, we will draw an isocost line, say I name it as a dash. So this cost line shows the same level of cost but different combinations of x1 and x2 the firm could have disposed, right? And here you can see by formulation or the way we draw x1 and x2 are more or less equal priced or more or less same costly. Okay. But if it was just a bit more flatter line, we can say that see, suppose this was the case. So here you can say that if the firm disposed the entire or utilized the entire cost for purchase of x1, it could have produced this. It could have used this much, and for x2 it would have used this thing. That means x2 is relatively cheaper as compared to x1. Okay. So that is the case we could have considered, guys. So here now we will see what is the new point that we are getting. So there is a tangency between isocost and isocost line. So we mark it as R dash. Say here we can mark it as R. So R dash is a point where the isocost line and isocost lines are intersecting. That means given the technology which is being represented by the isoquant and given the prices that is being represented by the price line or the isocost line, R dash is the point at which the firm could have produced at the technically efficient and minimal cost level. So now we'll try to see what, so this one is the isocost line. So here, if the firm operating at P could have achieved this point, but for that actually they need to move in a non-radial manner. So we'll see what is the point over here that is marked as R, and that was the optimal combination of x1 and x2 the firm could have combined. So in that case, of course, this firm has an inefficiency. Keeping the inefficiency, technical inefficiency aside, there is a distance between O R and OQ that is basically O and OQ, and we conceptualize that as allocative efficiency. Okay. So this can be named as efficiency, allocative efficiency. So as compared to technical efficiency, what allocative efficiency takes into account? It takes into account the price vector where here in this case it takes into account price of x1 and x2 while seeing the actual technically efficient outcome and how it is deviating from the cost minimization or outcome which takes into account our input prices. So now we'll see. So we had technical efficiency and we had allocative efficiency. Now we'll bring into this thing a new concept that is called economic efficiency. So economic efficiency, as the name suggests, it takes the overall economic aspects, both technical as well as the allocative aspect of the decision-making unit. So by formulation, we can consider it as OQ by OP into OR by OQ, where this one is our technical efficiency and this one is our allocative efficiency. So this OQ and OQ will cancel out. OQ by OP, that is basically the distance between OR and OP, basically how much it is deviating from a technically efficient and allocatively efficient input-output bundle. So this will give us an economic efficiency from an empirical point of view. Sometimes we can go beyond economic efficiency. Suppose you have data for more than one period and achieving economic efficiency throughout the period under consideration or over a period of time where we are bringing in the time dimension into the picture of our performance evaluation. We can call it dynamic efficiency that you will see in the literature. What is the main limitation of allocative efficiency and economic efficiency from an empirical point of view? Here we were conceptualizing our isocost line which is based on the prices of x1 and x2. But in reality, you will not be able to get this price value, and also even if you are fortunate enough to have price values of our inputs, sometimes market conditions may vary for firms. So sometimes some firms may have a higher bargaining power or some of them may have a lower bargaining power. So in that case, actually, you will not be able to use a ve

few more related concepts especially from a performance evaluation that in a frontier based performance evaluation.

One is allocative efficiency and the other one is tech economic efficiency where these three concepts are interrelated.

So from a very simple two inputs one output case as we have already discussed you can conceptualize the production frontier or technology set by using the concept of isocond.

So we'll be using an isocond framework. Say you have input one that is x1 here input 2 x2 over here.

So just to make our lives bit more easy we'll try to make both inputs and out both the inputs in in density form that for one unit of output how much input x1 and x2 are being used [snorts]

with that we'll be getting we can conceptualize a isocond say like is we name it as SS Sash and this isocone shows what is the level of or various combination of X1 and X2 that needs to be disposed or used from a production

point of view to produce one unit amount of single output that we are having that is Y.

So now coming back to the our performance evaluation the very first performance evaluation that we had it was the technical efficiency.

So now we need to see whether one observation say operating at this point producing one unit of output assume that way whether it is technically efficient or not. So revisiting the same concept what we have already discussed in this

context it is more of an input approach where firm is operating at this point say P. We need to see how much extra input the firm uses for producing the level of output that is y one unit and what is the deviation or the level

of inefficiency that it has from the frontier. So for that we'll conceptualize a framework where we are trying to reduce the input usage of both input one and input two that is x1 and x2. So we are trying to

reduce both x1 and x2 at the same rate. So here it can be named as radial contraction. But in case uh there can be a where you can reduce one input more proportionately than another input that will be a non-radial

uh contraction that you can consider. So here what we are doing we are connecting the point P with a line passing through origin. So that gives us an idea how much the firm P or how much the decision

making unit that is operating at point P is deviating from the potential outcome. So here you can see we mark this point on this isocond Q. And here you can see OP is the actual combination of X1 and X2 or the

intensities that firm is using. But if the firm was technically efficient or given the technology the firm could have produced same level of output by operating at point OQ but it is operating at point OP. So that will give us a value less than 1. That

means the firm operating at P is technically inefficient. And this ratio of OQ by OP will give you the level of inefficiency the firm operating at. So here we can see it is somewhere half of the U distance. So in some sense we can say

that firm can reduce the input intensities of x1 and x2 uh half or it could have reduced its inputs half as compared to the uh actual level of operation that it is going through prescendingly. So that shows the level of inefficiency or the

potential reduction that the firm could have done. So now we approach the same problem but from a different perspective.

Here what we are doing so far what we discussed it consists of only the actual amount of inputs being used for production purpose. One main problem is miss main component is missing that is the price or the cost of production.

Since both x1 and x2 will involve uh price say w1 and w2. We need to take into account the price of x1 and x2 into the picture and see given these prices how the firm is utilizing x1 and x2 for

the production process. So to plug in the price into the picture, we will draw a isocost line say I name it as a a dash.

So this is cost line shows the same level of cost but different combination of X1 and X2 the firm could have disposed right and here you can see uh by formulation or the way we draw X1 and X2

are more or less equal priced or more or less same costly. Okay. But if it was just bit more flatter line, we can say that uh see suppose this was the case. So here you can say that if the

firm disposed the entire uh or utilized the entire cost for purchase of uh X1, it could have produced this. It could have used this much and for X2 it would have used this thing. that means x2 is relatively cheaper as compared to u x1.

Okay. So that is the case we could have considered guys. So here now we will see what is the new point that we are getting. So there is a tangency between isocond and isocost line. So we mark it

as R dash. Say here we can mark it as R. So Rdash is a point where the isoc cost line and isoc lines are intersecting.

That means given the technology which is being represented by the ISO quant and given the prices that is being represented by the price line or the ISO cost line. Rdash is the point at which the firm could have produced at the

technically efficient and minimal cost level. So now we'll try to see what so this one is the isocost line. So here uh if the firm operating at P could have achieved this point but for that actually they need to move in a non-radial manner. So

we'll see what is the point over here that is marked as R and that was the optimal combination of X1 and X2 the firm could have combined.

So in that case of course this firm has an inefficiency. Keeping the inefficiency technical inefficiency aside there is a distance between O R and OQ that is basically O and OQ and we conceptualize that as allocative efficiency.

Okay. So this can be named as efficiency allocative efficiency. So as compared to technical efficiency what allocative efficiency takes into account? It takes into account the price vector where here in this case it takes into account price of X1 and X2 while seeing

the actual technically efficient outcome and how it is deviating from the cost minimization or outcome which takes into account our input prices.

So now we'll see. So we had technical efficiency and we had allocative efficiency. Now we'll bring into this thing a new concept that is called economic efficiency.

So economic efficiency as the name suggest it takes the overall economic aspects both technical as well as the allocative aspect of the decision making unit. So by formulation we can consider it as OQ by OP into O R by

OQ where this one is our technical efficiency and this one is our allocative efficiency. So this OQ and OQ will cancel out. O by OP that is basically the distance between OR and OP. Basically how much it is deviating

from a technically efficient and allocatively efficient input output bundle. So this will give us a economic efficiency from an empirical point of view.

Sometime we can go beyond economic efficiency. Suppose you have data for more than one period and achieving economic efficiency throughout the period under consideration or over a period of time where we are bringing in the time dimension into the picture of our

performance evaluation. We can call it as a dynamic efficiency that you will see it in the literature.

What is the main uh limitation of allocative efficiency and economic efficiency from empirical point of view?

Here we were conceptualizing our ISO cost line which is based on the prices of X1 and X2.

But in reality you will not be able to get this price price value and also even if you are fortunate fortunate enough to have price values of our uh inputs sometime market condition may vary for firms. So sometime some firms may have a

higher bargaining power or some of them may have a lower bargaining power. So in that case actually uh you will not be able to uh use a very fair values for price.

Sometime price may reflect something beyond or the uh point at which the firm operating and under particular technology or um under a given price may vary based on the level of bargaining power or the market condition that they are facing.

So in reality getting price data is very difficult or even if you get a price data. So making it as a standardized price data or if you have the time dimension as I was referring to it become even complicated because price

may keep on varying based on the level of inflation that we are having then you may have to adjust the prices based on uh the level of inflation so and so. So it become very complicated though economic efficiency is a very

comprehensive measure of performance especially from a frontier based performance evaluation approach. We will not be able to u do or give that much importance to this concept in our empirical approach mainly due to the non- aility of data.

So to summarize uh in today's session what we covered three very fundamental concepts in the context of uh production frontier based performance evaluation. We revisited our technical efficiency concepts. We saw the allocative efficiency how to define it given the price data that we are

having which we conceptualize using ISO con sorry ISO cost line and then we plugged in our new concept that is basically the economic efficiency which is basically the product of technical efficiency and allocative efficiency and we saw the later extensions of that in

terms of dynamic efficiency. Continuation to what we discussed that is technical efficiency, allocative efficiency and economic efficiency.

The same thing you can conceptualize in the context of two output, one input. So that will takes the form of production possibility frontier similar to this here one side you have y1 and y2 and say you're using one unit of uh

single input x and we can extend the same thing uh by using and price line of our y1 and y2 and that will give you a more or less uh similar concept what we had it in the context of allocative

efficiency here it it we'll be looking at from a revenue point of view and a firm say operating at this point it will be a radial expansion that the firm could to achieve by expanding both y1 and y2. Say here y1 y2

y1 star y2 star. So this will give you an idea about whether the firm is technically efficient or efficient from the revenue point of view or uh equally we can get an idea of economic efficiency in this context

also. In some cases some production may involve undesirable output as well. So we'll see the case of what will happen to our production frontier or technology set in the context of an undesirable output extending our understanding of isocond or the production possibility

set that I refer referred in the last session. So here say here I'm considering output Y that is basically the desirable output and Y U basically the undesirable output that we are referring to you can think how the production

possibility from here looks like in this context suppose you are having only one input to dispose here we can conceptualize our production frontier or empirical production frontier Okay, this so what why is it of a inverted U shape

here you can see assume Y as the desirable output say the value of output in the context and YU that is un undesirable output let us see this as the CO2 so here more the production of output, desirable output, you'll be getting

more and more undesirable output. But you can see after a point if you have even more undesirable output that may impact even the desirable output that you are referring to. Say we are taking the case of a car which emit a

particular level of um smoke or particular level of CO2 and consider Y as the mechanical efficiency or the distance or distance that being covered.

So in that case actually if the suppose you want to cover a particular amount of distance surely we'll have to compromise on the CO2 but beyond the point if the CO2 increases we'll not be able to reach the

particular level of distance. So with that actually we can get an inverted U-shaped u technology set like a technology set of this sort whatever region over here the this part it is basically the technology set that you can

conceptualize. So now we'll see how do we estimate how how do we claim whether a firm is technically efficient or not in this context. Surely we'll approach this from a uh data point of view at a later stage. But from a theoretical point of

view say one firm is operating at this stage. How do you say whether the firm is technically efficient or not? But surely looking at this uh point without having any reference to our uh potential or whatever we can get an idea

the firm is operating inefficiently because given the technology this firm could have produced uh any point on this frontier which will better off this firm.

So here now where to move whether I should move in this direction that increases the output but in that case actually you are keeping the undesirable output same level y u I say this one is y* n y i Right.

I So should I just increase my desirable output without focusing on the undesirable output? But given the kind of harm or negative externalities this undesirable output will make into our production framework we may have to compro we may have to compromise on some

amount of desirable output to reduce the undesirable output involved in the production process. So in that case what the empirical approach does is we can have a negative of yu right and then positive of the same actual yi that we are having.

So then what we try to do from origin we can have a point or a direction that reduces the undesirable output and increases the desirable output. Then what we do? We try to move from this actually observed outcome point

actually achieved outcome point. We try to move parallel to the line or the direction that we decided by taking the value of desirable output and minus of undesirable output. So that will take us somewhere here assume it is parall to this line

and this is the point where which could have we could have achieved given the technology. So I claim as again this point that we discussed in the uh last uh target. This point is more ideal where we are trying to

increase the desirable output as well as trying to minimize the undesirable output proportionately and this point or deviation from this point to this point will be considered as the the inefficiency or the level of inefficiency.

So when it comes to the durance model, we will see how to incorporate uh the undesirable output and desirable output and the normal inputs into the framework and see how to measure this distance and the how to conceptualize

how far the individual observations are deviating from their potential output. [music] [music]