This video shows how useful a good understanding of production duality can be. Starting with production maximisation and cost minimisation, this video explores everything you need to understand about production duality.
As in consumer’s theory (where consumption duality is analysed), the firm’s input decision has a dual nature. Finding the optimum levels of inputs, can not only be seen as a question of choosing the lowest isocost line tangent to the production isoquant (as seen when minimising cost), but also as a question of choosing the highest production isoquant tangent to a given isocost line (maximising production). In other words, having a cost function that sets a budget constraint, solving for the inputs allocation that gives the highest output.
The way to solve either problem is very similar: we look for the Lagrangian function and obtain first order conditions, then solve the system. When dealing with primal demand, that is, output maximisation, our Langrangian is our production function. When dealing with dual demand, that is, cost minimisation, our Lagrangian is our cost function.
Learn more by reading the dictionary entry.