Chapter 18 TECHNOLOGY.

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Presentation transcript:

Chapter 18 TECHNOLOGY

18.1 Inputs and Outputs Factors of production: inputs to production. Capital goods: inputs that are themselves produced goods. Financial capital: the money used to start up or maintain a business. Physical capital: produced factors of production.

18.2 Describing Technological Constraints Production set The set of all feasible combinations of inputs and outputs. Production function A function that associates given inputs with the maximum possible output. Gives the boundary of the production set. Isoquant The set of all possible combinations of inputs that are just sufficient to produce a given amount of output.

18.2 Describing Technological Constraints output y=f(x) Production set input

18.2 Describing Technological Constraints

18.3 Examples of Technology Fixed Proportions f(x1,x2)=min{x1,x2} x2 isoquants x1

18.3 Examples of Technology Perfect Substitutes f(x1,x2) =x1+x2 x2 isoquants x1

18.3 Examples of Technology Cobb-Douglas f(x1,x2) = Ax1ax2b

18.4 Properties of Technology Monotonicity (free disposal) Increase the amount of at least one of the inputs and output will increase. Convexity Two ways to produce y units of output: (x1, x2) and (z1, z2), their weighted average will produce at least y units of output.

18.4 Properties of Technology x2 isoquant x1

18.5 The Marginal Product Marginal product of factor 1: Similar to the concept of marginal utility.

18.6 The Technical Rate of Substitution The rate at which the firm has to substitute one input for another in order to keep output constant. Similar to the concept of marginal rate of substitution.

18.7 Diminishing Marginal Product Law of diminishing marginal product The marginal product of a factor will diminish as we get more and more of that factor. The law of diminishing marginal product applies only when all other inputs are being held fixed.

18.8 Diminishing Technical Rate of Substitution As we increase the amount of factor 1, and adjust factor 2 so as to stay on the same isoquant, the technical rate of substitution declines. Diminishing marginal product implies diminishing technical rate of substitution. Diminishing technical rate of substitution does not necessarily imply diminishing marginal product.

18.9 The Long Run and the Short Run In the short run, there will be some factors of production that are fixed at predetermined levels. In the long run, all the factors of production can be varied. y Y=f(x1, x2’) x1

18.10 Return to Scale Constant returns to scale tf(x1, x2) =f(tx1, tx2) Increasing returns to scale tf(x1, x2) < f(tx1, tx2) for all t>1 Decreasing returns to scale tf(x1, x2) > f(tx1, tx2) for all t>1

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