 What is meant by a production set? Actually the production set is a complete process that an entrepreneur or producer is going to take for the production of a given level of an output. So if a producer is going to produce a good that is called X or either it is called Y or it is called Z or it is called Y1 or Y2 and we can say that whatever it is, that means whether it is making a purza of a vehicle or making a special type of clothing or it is making a special type of crop in its field, whatever it is, with that one output and with that one output, whatever it is going to be that is called production set that will be utilized for today's topic. So if we say this is related to an output or an input and output relationship whatever it is going to be, that will be the production set. So production set is basically the all possible set of the feasible net output bundles and including the all required inputs. So firm when it is having any type of the activity to produce a particular level of the output that we are going to have in this diagram that might be the firm is having one Y1 or the Y2 or the Y3 but for this type of the setup now the firm has to decide that which type of the input the firm has to utilize. So the firm can utilize any type of the input to produce Y1, Y2 or the Y3 and we can see that here this is one curve that is showing the level of the output or we can say that it is the production possibility frontier or production possibility curve that shows that there are the two types of the output Y1 on X axis and Y2 on the Y axis. So these two combination of outputs are there and this is the curve that shows the combination of these two outputs but now the producer has the level that he has the capacity to produce either in this shaded area or he can produce on this line or this curve or he has the capacity to might be to produce out of this part. So the producer has the three areas this inside the shaded area just on the line and outside. So we say that if this function of the output level is just equal to the available resources to the producer in the sense or we can say all the production sets are such that they are just equal to the available resources or the inputs to the producer then the producer will be having the output level it will be the maximum level of the output through those resources or we can say the producer is having efficient level of production or the best opposite output against the inputs and out of this output level if on the right side this will not be achievable because it will be beyond the capacity and if it is in this shaded area it can be attainable but that will be the inefficient. So it means producer has the capacity to produce all these inefficient combinations and this efficient combination within the resources. If we come to this combination so we say that this function that we have shown on the right side if it is like this that it is less than zero then all the production sets they are equivalent description of that technological constraint and technological constraint means the all given resources and if this is technically possible that this set is having a value equal to zero it means then there is also a possibility that there can be the zero level of the output at the same level but this total setup it also shows that the production within the shaded area including the boundaries that can be provided by the producer or that can be the inefficient or at the same time the efficient at the only at the boundary level here comes one and important aspect that at the upper boundary that we have shown here this graph if the producer is producing just on this line then it is not possible for the producer to switch the inputs until and unless he has to sacrifice one resource for the other or one output for the other and this theory or this statement it is also called the theory of the Pareto optimality so the upper boundary is therefore the output efficient and that satisfies the equation that is set by the production sets