Title of talk: PRODUCTION THEORY FOR CONSTRAINED LINEAR ACTIVITY MODEL
Speaker: Prof. Somdeb Lahiri, PD Energy University, Gujarat, India.
Day, Date and Time: Tuesday, April 5, 2022, 4 PM to 5 PM.
Abstract: The purpose of the paper under discussion is to generalize the framework of activity analysis discussed in Villar (2003) and obtain similar results concerning solvability. We generalize the model due to Villar (2003), without requiring any dimensional requirements on the activity matrices and by introducing a model of activity analysis in which each activity may (or may not) have a capacity constraint i.e. a maximum level at which the activity can operate. This may be one way to accommodate meaningful non-linearities similar to that considered for input-output analysis in Sandberg (1973). In Sandberg (1973), the input-output coefficients were assumed to be differentiable, which is very likely an approximation of the more realistic representation in which the input-output coefficients are piecewise constant. Minor, technical increments on the solvability result in Sandberg (1973) can be found in Chander (1983) and some references therein. Undoubtedly, piecewise constant input-output constants are more difficult to deal with mathematically than differentiable ones. Non-linearities are much easier to represent in the framework of linear activity analysis by introducing upper bounds-whenever there is a capacity constraint-for the levels at which each such activity may operate. We do this by introducing a model of activity analysis in which each activity may (or may not) have a capacity constraint. It seems that in this significantly more general framework we are able to obtain the desired results concerning solvability and existence of an equilibrium price vector under weaker assumptions than the corresponding requirements in Villar (2003). We also provide proofs of two versions of the Non-Substitution Theorem that establish the existence of “efficiency price-vectors” as a joint product. However, our Non-Substitutions Theorems- in spite of the generality of our model as compared to the one due to Villar (2003)- requires that if there are capacity constraints, then there is a minimal subset of the set of capacity constrained activities that are always used up to full capacity, for the production of all producible final demand vectors. Further, these capacity constrained activities are the only ones whose capacities are binding for some producible final demand vector.
(Please find attached a pdf on talk details and related reference papers.)
Speaker Bio:
Prof. Somdeb Lahiri obtained a Ph.D in Economics from the University of Minnesota in 1986, but more importantly-as his lived life suggests-he obtained M.Stat (Hons.) from Indian Statistical Institute, Kolkata. He is currently a Professor of Economics at the School of Petroleum Management, PD Energy University (PDEU). His research interests are in decision (making) theory, decision analysis.