# Part Eighteen

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﻿Section Eighteen Technology

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Technologies An innovation is a procedure by which information sources are changed over to a yield. E.g. work, a PC, a projector, power, and programming are being consolidated to create this address.

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Technologies Usually a few innovations will deliver a similar item - a writing board and chalk can be utilized rather than a PC and a projector. Which innovation is "ideal"? How would we look at advances?

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Input Bundles x i signifies the sum utilized of info i; i.e. the level of info i. An information package is a vector of the info levels; (x 1 , x 2 , … , x n ). E.g. (x 1 , x 2 , x 3 ) = (6, 0, 9 × 3).

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Production Functions y signifies the yield level. The innovation's creation work expresses the greatest measure of yield conceivable from an information package.

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Production Functions One information, one yield Output Level y = f(x) is the creation work. y' y' = f(x') is the maximal yield level reachable from x' input units. x' x Input Level

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Technology Sets A creation plan is an info package and a yield level; (x 1 , … , x n , y). A generation plan is practical if The gathering of all achievable creation arrangements is the innovation set .

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Technology Sets One information, one yield Output Level y = f(x) is the creation work. y' y' = f(x') is the maximal yield level reachable from x' input units. y" y" = f(x') is a yield level that is practical from x' input units. x' x Input Level

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Technology Sets The innovation set is

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Technology Sets One info, one yield Output Level y' The innovation set y" x' x Input Level

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Technology Sets One information, one yield Output Level Technically proficient arrangements y' The innovation set Technically wasteful arrangements y" x' x Input Level

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Technologies with Multiple Inputs What does an innovation look like when there is more than one info? The two info case: Input levels are x 1 and x 2 . Yield level is y. Assume the creation capacity is

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Technologies with Multiple Inputs E.g. the maximal yield level conceivable from the info package (x 1 , x 2 ) = (1, 8) is And the maximal yield level conceivable from (x 1 ,x 2 ) = (8,8) is

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Technologies with Multiple Inputs Output, y x 2 (8,8) (8,1) x 1

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Technologies with Multiple Inputs The y yield unit isoquant is the arrangement of all information packages that yield at most a similar yield level y.

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Isoquants with Two Variable Inputs x 2 y º 8 y º 4 x 1

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Isoquants with Two Variable Inputs Isoquants can be charted by including a yield level hub and showing each isoquant at the tallness of the isoquant's yield level.

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Isoquants with Two Variable Inputs Output, y º 8 y º 4 x 2 x 1

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Isoquants with Two Variable Inputs More isoquants enlighten us all the more regarding the innovation.

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Isoquants with Two Variable Inputs x 2 y º 8 y º 6 y º 4 y º 2 x 1

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Isoquants with Two Variable Inputs Output, y º 8 y º 6 y º 4 x 2 y º 2 x 1

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Technologies with Multiple Inputs The entire gathering of isoquants is the isoquant outline The isoquant guide is comparable to the creation work - each is the other. E.g.

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Technologies with Multiple Inputs x 2 y x 1

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Technologies with Multiple Inputs x 2 y x 1

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Technologies with Multiple Inputs x 2 y x 1

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Technologies with Multiple Inputs x 2 y x 1

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Technologies with Multiple Inputs x 2 y x 1

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Technologies with Multiple Inputs x 2 y x 1

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Technologies with Multiple Inputs y x 1

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Technologies with Multiple Inputs y x 1

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Technologies with Multiple Inputs y x 1

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Technologies with Multiple Inputs y x 1

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Technologies with Multiple Inputs y x 1

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Technologies with Multiple Inputs y x 1

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Technologies with Multiple Inputs y x 1

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Technologies with Multiple Inputs y x 1

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Technologies with Multiple Inputs y x 1

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Technologies with Multiple Inputs y x 1

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Cobb-Douglas Technologies A Cobb-Douglas creation capacity is of the shape E.g. with

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Cobb-Douglas Technologies x 2 All isoquants are hyperbolic, asymptoting to, however failing to touch any pivot. x 1

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Cobb-Douglas Technologies x 2 All isoquants are hyperbolic, asymptoting to, yet failing to touch any pivot. x 1

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Cobb-Douglas Technologies x 2 All isoquants are hyperbolic, asymptoting to, however failing to touch any hub. x 1

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Cobb-Douglas Technologies x 2 All isoquants are hyperbolic, asymptoting to, yet failing to touch any pivot. > x 1

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Fixed-Proportions Technologies A settled extents generation capacity is of the frame E.g. with

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Fixed-Proportions Technologies x 2 x 1 = 2x 2 min{x 1 ,2x 2 } = 14 7 min{x 1 ,2x 2 } = 8 4 2 min{x 1 ,2x 2 } = 4 8 14 x 1

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Perfect-Substitutes Technologies An immaculate substitutes creation capacity is of the shape E.g. with

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Perfect-Substitution Technologies x 2 x 1 + 3x 2 = 18 x 1 + 3x 2 = 36 x 1 + 3x 2 = 48 8 6 All are straight and parallel 3 x 1 9 18 24

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Marginal (Physical) Products The minimal result of info i is the rate-of-progress of the yield level as the level of information i changes , holding all other info levels altered . That is,

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Marginal (Physical) Products E.g. in the event that then the minor result of info 1 is

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Marginal (Physical) Products E.g. in the event that then the minor result of info 1 is

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Marginal (Physical) Products E.g. in the event that then the peripheral result of information 1 is and the minor result of info 2 is

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Marginal (Physical) Products E.g. on the off chance that then the minor result of information 1 is and the negligible result of info 2 is

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Marginal (Physical) Products Typically the minimal result of one information relies on the sum utilized of different sources of info. E.g. assuming then, if x 2 = 8, and if x 2 = 27 then

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Marginal (Physical) Products The minimal result of information i is decreasing on the off chance that it gets to be littler as the level of information i increments. That is, if

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Marginal (Physical) Products E.g. assuming then and

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Marginal (Physical) Products E.g. assuming then thus

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Marginal (Physical) Products E.g. assuming then thus and

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Marginal (Physical) Products E.g. assuming then thus and Both minor items are lessening.

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Returns-to-Scale Marginal items depict the adjustment in yield level as a solitary information level changes. Comes back to-scale portrays how the yield level changes as all info levels change in direct extent ( e.g. all info levels multiplied, or divided).

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Returns-to-Scale If, for any information package (x 1 ,… ,x n ), then the innovation portrayed by the creation work f shows steady comes back to-scale . E.g . (k = 2) multiplying all information levels copies the yield level.

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Returns-to-Scale One information, one yield Output Level y = f(x) 2y' Constant comes back to-scale y' x' 2x' x Input Level

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Returns-to-Scale If, for any info package (x 1 ,… ,x n ), then the innovation shows consistent losses to-scale . E.g . (k = 2) multiplying all information levels not as much as duplicates the yield level.

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Returns-to-Scale One info, one yield Output Level 2f(x') y = f(x) f(2x') Decreasing comes back to-scale f(x') x' 2x' x Input Level

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Returns-to-Scale If, for any information package (x 1 ,… ,x n ), then the innovation displays expanding comes back to-scale . E.g . (k = 2) multiplying all info levels dramatically increases the yield level.

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Returns-to-Scale One information, one yield Output Level Increasing comes back to-scale y = f(x) f(2x') 2f(x') f(x') x' 2x' x Input Level

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Returns-to-Scale A solitary innovation can "locally" display distinctive comes back to-scale.

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Returns-to-Scale One information, one yield Output Level y = f(x) Increasing comes back to-scale Decreasing comes back to-scale x Input Level

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Examples of Returns-to-Scale The ideal substitutes generation capacity is Expand all info levels proportionately by k. The yield level gets to be

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Examples of Returns-to-Scale The ideal substitutes creation capacity is Expand all info levels proportionately by k. The yield level gets to be

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Examples of Returns-to-Scale The ideal substitutes generation capacity is Expand all information levels proportionately by k. The yield level turns into The ideal substitutes creation work displays consistent comes back to-scale.

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Examples of Returns-to-Scale The ideal supplements creation capacity is Expand all information levels proportionately by k. The yield level gets to be

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Examples of Returns-to-Scale The ideal supplements generation capacity is Expand all information levels proportionately by k. The yield level gets to be

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Examples of Returns-to-Scale The ideal supplements creation capacity is Expand all info levels proportionately by k. The yield level turns into The ideal supplements generation work shows consistent comes back to-scale.

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Examples of Returns-to-Scale The Cobb-Douglas creation capacity is Expand all info levels proportionately by k. The yield level gets to be

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Examples of Returns-to-Scale The Cobb-Douglas generation capacity is Expand all information levels proportionately by k. The yield level gets to be

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Examples of Returns-to-Scale The Cobb-Douglas creation capacity is Expand all information levels proportionately by k. The yield level gets to be

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Examples of Return