Lecture_14_Technology

Lecture_14_Technology - Lecture 14: Technology c 2008 Jerey...

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Lecture 14: Technology c 2008 Je/rey A. Miron Outline 1. Introduction 2. Describing Technological Constraints 3. Examples 4. Properties of Technology 5. The Marginal Product 6. The Technical Rate of Substitution 7. The Long Run versus the Short Run 8. Returns to Scale 1 Introduction We have now developed the demand side of the market; in particular, we modeled how consumers make choices about what goods to buy and consume. The second step in the course is to model the supply side; roughly speaking, we are modeling how the goods consumers purchase came into being and became available for purchase and consumption. We will do this in several steps. We &rst consider the constraints that all pro- duction decisions must face; we refer to this as the technology. We then discuss the objective functions that owners of this technology might be attempting to maximize, and we characterize the decisions that lead this maximization. We will be able to summarize these decisions in supply curves, just as we summarized the decisions of consumers in demand curves. Then, in the third part of the course, we put demand and supply together to analyze equilibria, policy, and so on. 1
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2 Describing Technological Constraints The model of technology assumes the following: Various inputs exist in the world. These inputs are goods and services that can be combined in some way to lead to other goods called outputs. What are these inputs? Pre-existing produced goods, labor, capital, and land, among others. Nature imposes some rules: only certain combinations of inputs are feasible ways to produce a given amount of output. The combinations of inputs and outputs that are technologically feasible is called the production set. 2
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Graph: A Production Set y 2 p x boundary = production function 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 x y The boundary of this set is called the production function. The graph above as- sumes a production process with only one input, but that is solely for inconvenience. In general the technology for producing goods requires many inputs. One way to depict the technological possibilities when production requires two inputs is via isoquants: 3
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Graph: Isoquants 4 = x 1 = 2 y 1 = 2 2 = x 1 = 2 y 1 = 2 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 x1 x2 An isoquant represents all combinations of two inputs that produce a given
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Lecture_14_Technology - Lecture 14: Technology c 2008 Jerey...

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