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# Ch10 - Chapter 10 Firms and Technology 10.1 Introduction So...

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Chapter 10: Firms and Technology 10.1: Introduction So far we have worked in a world without production – in a pure-exchange world where people have initial endowments and might want to exchange them. We must now add production to the story. Production is important in the real world. Production exists because people see that there are profits to be made by producing things that do not exist but which people want to buy. Usually, but rather conventionally, we say that production is done by firms. Firms are there to produce. Indeed we can define a firm as an organisation that buys certain things, does something to them and then sells the resulting product. Rather trivially we can say that a firm buys inputs and converts the inputs into output through some production process and then sells the resulting output. Usually a firm produces several outputs using several inputs, but we will be able to do the analysis that we need with a firm that produces one output with two inputs. All the results that we derive can be extended but this (one output, two input) world is sufficiently simple to make the analysis relatively easy. The purpose of this chapter is to explore and define the relationships between the output and the two inputs. In the subsequent chapters we explore the implications. 10.2: Production Functions In this chapter a firm is an organisation that buys two inputs and transforms them into an output. Let us denote the two inputs by input 1 and input 2, and let us denote the quantities of each by q 1 and q 2 . Let us denote the quantity of output produced by y . Let us assume that both the inputs are genuine inputs in the sense that the higher the quantity of each used the higher is the output of the firm. Central to the firm is the production process – which converts inputs into output. In general this can be described by a production function which we can write as y = f(q 1 ,q 2 ) (10.1) and where the function is increasing in both its arguments. We will find it useful to describe this function in two ways – as there are, in a sense, two dimensions to the description of the production process. The first is the relationship between the two inputs in the production process for a given scale of production; the second is the relationship between the scale of the inputs and the scale of the output. To understand the relationship between the two inputs in the production process it is useful to introduce the concept of an isoquant . An isoquant is a curve in (q 1 , q 2 ) space for which the level of output is constant. It is formally defined by f(q 1 ,q 2 ) = constant We shall study this intensively later.

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To understand the relationship between the scale of the inputs and the scale of the outputs, we ask what happens when we change the scale of production – moving from (q 1 , q 2 ) to (sq 1 , sq 2 ) – where s is some scaling factor, that is, we mutiply the quantity of both inputs by s . What happens?
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Ch10 - Chapter 10 Firms and Technology 10.1 Introduction So...

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