XIV. Technology
XIV. a. Definitions
- Technology = process by which inputs converted to output/final product
- Types of input: labour + capital
- Possibility of using several technologies for producing same product (i.e.,
substituting blackboard & chalk with computer & projector)
- Comparing/evaluating technologies
XIV. b. The production function
- xi denoting amount used of input I (i.e., level of input i)
- Input bundle = vector input levels (x1, x2, …, xn)
o Example: X = xlabour, xcapital
- Y denoting output level
- Technology production function stating maximum amount of output possible
from input bundle
y = f (x1, x2, …, xn)
o Note: any point below red line = feasible level below maximum possible
level of output
XIV. c. Isoquants
- Technology with more than one input
o Two input case: input levels x1 & x2 with output level y & production
function y = f (x1, x2)
, - Isoquant for y-unit output = set of all input bundles yielding same output level
y (see black line below)
- Comparing absolute value of isoquants giving information about technology
- Complete collection of isoquants of technologies with multiple inputs =
isoquant map ( production function)
XIV. d. Production functions
1) Cobb-Douglas technologies
- Cobb-Douglas production function
a a a
y= A x 1 x2 ×… × x n with A = multiplier (constant)
1 2 n
- All isoquants hyperbolic asymptoting (= converging) to without touching axis
(= impossibility producing output without any inputs)
2) Fixed proportion technologies
- Fixed proportion function: y=min{a1 x1 , a2 x2 , … , an x n }
- Output determined by “recipe” fixing proportions
- Possible output determined by minimum amount of each input required
o Note: case of perfect complements
3) Perfect substitutes technologies
- Perfect substitutes production function: y=a1 x 1 +a2 x 2 , …+ an x n with a =
coefficients
XIV. a. Definitions
- Technology = process by which inputs converted to output/final product
- Types of input: labour + capital
- Possibility of using several technologies for producing same product (i.e.,
substituting blackboard & chalk with computer & projector)
- Comparing/evaluating technologies
XIV. b. The production function
- xi denoting amount used of input I (i.e., level of input i)
- Input bundle = vector input levels (x1, x2, …, xn)
o Example: X = xlabour, xcapital
- Y denoting output level
- Technology production function stating maximum amount of output possible
from input bundle
y = f (x1, x2, …, xn)
o Note: any point below red line = feasible level below maximum possible
level of output
XIV. c. Isoquants
- Technology with more than one input
o Two input case: input levels x1 & x2 with output level y & production
function y = f (x1, x2)
, - Isoquant for y-unit output = set of all input bundles yielding same output level
y (see black line below)
- Comparing absolute value of isoquants giving information about technology
- Complete collection of isoquants of technologies with multiple inputs =
isoquant map ( production function)
XIV. d. Production functions
1) Cobb-Douglas technologies
- Cobb-Douglas production function
a a a
y= A x 1 x2 ×… × x n with A = multiplier (constant)
1 2 n
- All isoquants hyperbolic asymptoting (= converging) to without touching axis
(= impossibility producing output without any inputs)
2) Fixed proportion technologies
- Fixed proportion function: y=min{a1 x1 , a2 x2 , … , an x n }
- Output determined by “recipe” fixing proportions
- Possible output determined by minimum amount of each input required
o Note: case of perfect complements
3) Perfect substitutes technologies
- Perfect substitutes production function: y=a1 x 1 +a2 x 2 , …+ an x n with a =
coefficients
