Technology production function, an introduction*

ForNeoclassical economics a firm faces technological change in terms that certain combinations of inputs produce a given amount of output. Examples of technology are defined according to relationships (or combination) between inputs such as fixed proportion and perfect substitution. Then, the idea of technology is a list of the feasible production plans resulting for combination of inputs.

In this framework technology present two properties: i) it is monotonic which means that if you are producing 10 units and you increase at least one of the inputs you should be able to produce at least 10 units;ii) it is convex which means that if you can produce 10 units by two different combinations of inputs, you can produce at least 10 units by weighted average of those twocombinations.

Given the monotonic andconvexity properties,theproduction process hastwo important economylaws,the diminishing marginal product and the diminishing technical rate of substitution. The first one indicates that when an input increases,production increases but a decreasing rate; the second one, increasing an input and decreasing other input can keep production onthe same level but therate of technical substitution will decrease.

Clearly, thelaws mentioned above apply when firmscannot change at least one factor of production.This happens inthe short run while in the long run all factors can be varied. Then, technology can have different kinds of relationship between variations of allinputs and the output.This is named 'returns to scale´ and economy models usually assumeconstant returns to scale in the long run where inputs and outputs change at the same proportion (convexity assumption).

This theory allows us to understand what technology makes in the production process. The role of the technology is to definethe relationship between inputs and outputs (substitubility or complementarity), increasing outputs restricted by economic laws and time. Then, the optimization problem is to achieve the biggest output a given level of inputs.

This is a shortexplanation about technology and economy based onthestandard microeconomic theory. This model is ourstartingpoint to introduce new approaches to understand thetechnological change.

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