Question

Using a model of production isoquant curves and isocost curves explain how a firm with a Cobb-Douglas production function will meet its quota for producing a necessary level of output while minimizing costs. How would this firm choose among competing production technologies or change its production when it implements an improved technology (innovation)?

Answer 1

The Cobb Douglas production function is normally CRS in nature. This means that if we double inputs into the production process, we exactly double outputs. Now in case the objective is to minimize costs then the firm will consider the dual problem whereby it minimizes costs subject to a desired level of output. The calculations for the same are as follows. Now if a technology innovation is introduced then this will modify the nature of the production function with now a new component for technology and will then minimize costs subject to the modified production function. This is shown in the second section below. Thus initially below we minimize costs subject to a production function of a particular Cobb Douglas form We get optimal K and L this way. With the introduction of new technology, the production function nature changes and so we minimize costs subject to a new production function with technology.