Microeconomics 7: Technology, production and costs

Question 1

Describe technology’s relationship with production function

Answer 1

• We can view technology as a constraint on the
  firm’s behaviour – it defines what, at the present
  time, a firm can produce for given inputs.
  – Technology converts inputs into output.
• The inputs are factors of production:
  – labour (the input of workers)
  – capital (machinery, buildings and other man-made inputs)
  – land (including other naturally-occurring inputs).
• We will generally denote output as y and inputs
  as x1, x2, …

Question 2

Describe the ‘production function’

Answer 2

The production function defines the maximum
output possible for given quantities of inputs
* It is the boundary of the production set, which
includes all points that can be produced for
given quantities of inputs.
* We will often use examples with two inputs –
either y = f(x1, x2) using general inputs x1 and
x2, or y = f(L, K) using labour L and capital K.
* This model shows the production function
and set with a single input, y = f(x):
“x”-axis and “y”-axis with a slope with positive gradient but negative d^2 y / dx^2

Question 3

Describe ‘isoquants’

Answer 3

• With two inputs, we can illustrate production
  using isoquants.
• A single isoquant identifies all combinations of
  inputs that produce a given amount of output.
• They are most commonly drawn as smooth
  and convex
  Graph with “x1”-axis and y-axis, “x2” and parallel convex lines in the graph, where the one closest to origin is “y1” and the next closest is “y2” and so on

Question 4

Describe & explain the concept of ‘fixed proportion’ in the production function

Include graph

Answer 4

e.g. any number of machines can be used, but each machine needs exactly one worker to operate it, and additional workers cannot make anything without another machine
- We want an equal number of workers and machines
- What determines the level of production is the minimum of the number of machines and the number of workers
- If each worker and machine together produce one unit of output, the production function is f(x1,x2) = min{x1,x2}
Graph with “x1”-axis and y-axis, “x2” with parallel ‘L-shaped’ curves, the one closest to the origin is “y1”, the next one along is “y2” and so on
- With a cost-minimising firm with production function f(x1,x2) = min{x1,2x2}, the firm won’t produce equal quantities of each factor; the production function requires half a unit of factor 2 and one unit of factor 1 to produce one unit of output, so the firm will use half as much factor 2.
The term 2x2 does not mean 2 units of factor 2 are needed for every unit of output. Instead, it reflects that factor 2 contributes double the amount per unit. f 𝑥2= 0.5, then 2x2=1, matching x1=1…