Chapter 12: Technology

Question 1

A technology

Answer 1

A technology is a process by which inputs are converted to an output.
Inputs (x1, x2, …, xn) to production are called factors of production: * land * labor * capital * raw materials

Question 2

production set.

Answer 2

The set of all combinations of inputs and outputs y that comprise a technologically feasible way to produce is called a production set.

Question 3

production plan

Answer 3

A production plan is an input bundle and an output level (x1, x2, …, xn, y) and
is feasible if: y ≤ f (x1, x2, …, xn)

Question 4

An isoquant

Answer 4

An isoquant is the set of all input bundles that yield at most the same output
level y.

Question 5

( Fixed-proportions (Leontief) production function )

Answer 5

n economics, the Leontief production function or fixed proportions production function is a production function that implies the factors of production which will be used in fixed (technologically pre-determined) proportions, as there is no substitutability between factors.

Question 6

Monotonicity:
(properties)

Answer 6

Monotonicity:
* If you increase the amount of at least one input, you produce at least as
much output as before.
* Monotonicity holds because of free disposal, that is, the firm can free
dispose of any extra inputs.

Question 7

Convexity:
(properties)

Answer 7

• If y = f (x1, x2) = f (z1, z2), then f (tx1 + (1 − t)z1,tx2 + (1 − t)z2) ≥ y for any t ∈ [0, 1].
• If you have two ways, (x1, x2) and (z1, z2), to produce y units of output, the weighted average will produce at least y units of output.

Question 8

The technical rate of substitution

Answer 8

The technical rate of substitution measures the trade-off between two inputs in production. It measures the rate at which the firm will have to substitute
one input for another in order to keep output constant.

Question 9

The long run and the short run

Answer 9

In the long run, all the factors of production can be varied.

In the short run, some factors of production are fixed. A firm is restricted in some way in its choice of at least one input level.

Question 10

Returns to scale

Answer 10

Returns to scale describes how the output level changes as all input levels change in direct proportion (e.g. all input levels doubled, or halved).

• then the technology described by the production function f exhibits constant
  returns-to-scale.
• then the technology described by the production function f exhibits increasing
  returns-to-scale.
• then the technology described by the production function f exhibits decreasing
  returns-to-scale.

Question 11

Properties of technology

Answer 11

• Monotonicity:
• Convexity

Question 12

marginal product of input 1 is

Answer 12

is the rate-of-change of the output level as the level of input 1 changes, holding all other input levels fixed.

Question 13

(diminishing
TRS).

Answer 13

Strict convexity implies that the TRS increases as x1 increases