Technology Production And Costs Flashcards
Isoquant
Identifies all combinations of inputs (FOP) that produce a given output.
Fixed proportion isoquant
Technology is inflexible, so we want an equal number of workers and machines.
E.g each machine needs one worker to operate it, and additional workers cannot impact.
So what determines level of production for fixed proportion isoquants, and how can we express it in the production function.
Level of production is determined by the minimum number of machines and the number of workers needed to produce output y.
f(x₁,x₂)=min{x₁,x₂}
What does fixed proportion isoquants look like?
L shape (just like perfect complements diagram in consumer choice)
Because the 2 inputs are essentially perfect complements, need one for the other otherwise valueless.
Perfect substitutes isoquant, and how is this expressed in the production function.
Easily switch between inputs
Example: any machine or any worker can produce one unit of output per hour.
F(x₁,x₂)=x₁+x₂
What does the perfect substitutes isoquant look like?
Downward sloping straight.
Express CD function including technology
What happens if A increases
f(x₁,x₂) =Ax₁to the v x₂ to the 1-v
A represents tech. I.e if A increases, we can produce more output with same inputs.
Properties/assumptions about technology
Monotonicity
Free disposal
Convexity
Monotonicity assumption in technology
If we increasing quantity of at least one input without reducing the other, you produce at least as much as before.
Free disposal assumption in technology
Unwanted inputs can be disposed costlessly, so having more of any input can never be harmfuL.
Convexity assumption in technology
If there are 2 different ways of producing a given output, a weighted average of the 2 will produce at least the same amout.
Technical rate of substitution
How much more of one factor we need to add following a reduction in the other factor, to keep output constant.
How is TRS represented graphically
Slope of the isoquant.
TRS formula
dx₂/dx₁ = -MP₁/MP₂
How do we get this equation?
We get marginal product by differentiating prod function.
MP₁dx1 + MP₂dx₂
Then, since for TRS we want to hold output constant, marginal product=0.
MP₁dx1 + MP₂dx₂ = 0
Rearrange to make TRS
dx₂/dx₁ = -MP₁/MP₂
Is TRS usually diminshing, constant, or increasing
Diminishing technical rate of substitution i.e
As we keep reducing one factor, we need to increase amounts of the other factor to hold output constant
Returns to scale example slide 23.
Once we get t to the a+b, what do we do from there?
We now have 3 cases.
a+b> 1 , increasing returns
Etc.
Short run vs long run production assumption (same as last year)
Long run FOP variable
SR at least one is fixed (usually capital)
How to express the fixed factor in the short run
(Let factor 2 x₂ be fixed)
y = f(x₁,xbar₂)
Summary to cover
Production function
Isoquants
Returns to scale
SR LR
