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Section Eighteen Technology

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.

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?

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).

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

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

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 .

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

Technology Sets The innovation set is

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

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

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

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

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

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.

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

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.

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

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

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

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

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.

Technologies with Multiple Inputs x 2 y x 1

Technologies with Multiple Inputs x 2 y x 1

Technologies with Multiple Inputs x 2 y x 1

Technologies with Multiple Inputs x 2 y x 1

Technologies with Multiple Inputs x 2 y x 1

Technologies with Multiple Inputs x 2 y x 1

Technologies with Multiple Inputs y x 1

Technologies with Multiple Inputs y x 1

Technologies with Multiple Inputs y x 1

Technologies with Multiple Inputs y x 1

Technologies with Multiple Inputs y x 1

Technologies with Multiple Inputs y x 1

Technologies with Multiple Inputs y x 1

Technologies with Multiple Inputs y x 1

Technologies with Multiple Inputs y x 1

Technologies with Multiple Inputs y x 1

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

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

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

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

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

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

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

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

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

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,

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

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

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

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

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

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

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

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

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

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

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).

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.

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

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.

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

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.

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

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

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

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

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

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.

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

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

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.

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

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

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

Examples of Return

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