Lecture 6 - Technology Flashcards
(18 cards)
Production Functions
- y denotes the output level
- The technology’s production function states the maximum amount of output possible from an input bundle
y = f(x)
Is the production function
y’ = f(x’)
Is the maximal output level obtained from x’ input units
Production plan
Is an input bundle and an output level
Technology Set
The collection of all feasible production plans is the technology set
y’’ = f(x’)
Is an output level that is feasible from x’ input units
Isoquant Map
- The complete collection of isoquants is the isoquant map
- The isoquant map is equivalent to the production function
Cobb Douglas technologies
All isoquants are hyperbolic asymptoting to but never touching any axis
Marginal (physical) Products
- The marginal product of input is the rate of change of the output level as the level of input changes, holding all other input levels fixed
- Typically the marginal product of one input depends upon the amount used of other inputs
- The marginal product of input is diminishing if it becomes smaller as the level of input increases
Technical rate of substitution
- The slope is the rate at which input 2 must be given up as input 1’s level is increased so as not to change the output level
- The slope of an isoquant is its technical rate of substitution
A well behaved technology is
Monotonic and convex
Long run
- Is the circumstance in which a firm is unrestricted in its choice of all input levels
- A useful way to think of the long run is that the firm can choose as it pleases in which short run circumstance to be
Short run
- Is a circumstance in which a firm is restricted in some way in its choice of at least 1 input level
- There are many possible short runs
- Examples of restrictions that place a firm into a short run: temporarily being unable to install or remove machinery, being required by law to meet affirmative action quotas, having to meet domestic content regulations
Technology
A technology is a process by which inputs are converted to an output e.g. labour, capital
Input bundle
An input bundle is a vector of the input levels
Technology with multiple inputs
- The y output unit isoquant is the set of all input bundles that yield at most the same output level y
- More isoquants tell us more about the technology
Returns to scale
A single technology can locally exhibit different returns to scale
Examples of returns to scale
- The perfect substitutes production function exhibits constant rts
- The perfect complements production function exhibits constant rts
- The Cobb Douglas technology’s rts is:
- constant if a1 +…+ an = 1
- increasing if a1 +…+ an > 1
- decreasing if a1 +…+ an < 1