Chapter19TechnologyKeyConceptProductionfunctionOn.pptVIP

Chapter 19 Technology Key Concept: Production function On production functions, we could define some concepts which has close parallels in consumer theory. MP MU MRTS MRS RTS Chapter 19 Technology First understand the technology constraint of a firm. Later we will talk about constraints imposed by consumers and firm’s competitors (the demand curve faced by the firm, the market structure) Inputs: labor and capital Inputs and outputs measured in flow units, i.e., how many units of labor per week, how many units of output per week, etc. Consider the case of one input (x) and one output (y). To describe the tech constraint of a firm, list all the technologically feasible ways to produce a given amount of outputs. The set of all combinations of inputs and outputs that comprise a technologically feasible way to produce is called a production set. A production function measures the maximum possible output that you can get from a given amount of input. Fig. 18.1 Isoquant is another way to express the production function. It is a set of all possible combinations of inputs that are just sufficient to produce a given amount of output. Isoquant looks very much like indifference curve, but you cannot label it arbitrarily, neither can you do any monotonic transformation of the label. Some useful examples of production function. Two inputs, x1 and x2. Fixed proportion (perfect complement): f(x1,x2)=min{x1,x2} Fig. 18.2 Perfect substitutes: f(x1,x2)=x1+x2 Fig. 18.3 Cobb-Douglas f(x1,x2)=A(x1)a(x2)b, cannot normalize to a+b=1 arbitrarily Some often-used assumptions on the production function Monotonicity: if you increase the amount of at least one input, you produce at least as much output as before Monotonicity holds because of free disposal, that is, can free dispose of any extra inputs Convexity: if y=f(x1,x2)=f(z1,z2), then f(tx1+(1-t)z1,tx2+(1-t)z2)?y for any t?[0,1] Fig. 18.4 Some terms often used to describe the production function Marginal product: operate at