Production Functions Flashcards
What are firms?
A firm is an organisation that converts input like labour, materials and into outputs

What do we assume about firms?
we assume firms want to profit maximise.
Ignore potential conflicts between managers and owners
Ignore non profit motives
Profit formula?
Profit = Revenue - Cost
Revenue formula?
Revenue = Price * Quantity
What is the cost?
What a firm pays for inputs
To maximise profits, a firm must what?
A firm must produce efficiently to maximise profits
How does a firm produce efficiently
If it cannot produce more output for a given quantity of inputs
What is a production function?
Summary of the various ways a firm can efficiently transform inputs into outputs
What does the production function show?
Production functions shows only the combination of inputs that produce maximum amount of output
What is the production function assuming L and K are the only inputs
Labour (L) Capital (K)
q = f(L, K)
In what time period can a firm more easily adjust its inputs?
In the long run
What is the short run?
A period of time so brief that at least one factor of production is fixed
What is the long run
Period of time where all inputs are variable
What do we assume in the short run about factors of production specifically?
Capital is a fixed input and labour is a variable input
What is the short run production function?
What is the output q also called in the SR production function!?
The total product of labour
Definition of the total product of labour?
The amount of output that a given amount of labour can produce holding the quantity of other inputs fixed
What is the marginal product of labour?
The additional output produced by an additional unit of labour - holding all other factors constant
Formula for MPL?
What is the average product of labour ?
Ratio of output to the amount of labour employed
q/L
What is the law of diminishing marginal returns?
If a firm keeps increasing output, holding all other inputs and tech constant, the corresponding increases in output eventually become smaller
What does the law of diminishing marginal returns mathematically mean?
Is the LDMR a law?
The law of diminishing marginal utility is an empirical regularity rather than a law
The typical shape of production functions is in part due to what?
The Law of DMR
What does the production function described
How much output can be produced from various combinations of inputs
If there are just 2 inputs, capital and labour, the production function is…?
q = f(L,K)
What is an isoquant?
And isoquant shows the combinations of inputs that will produce a specific level of output
What are the properties of isoquants?
Isoquants have similar properties to indifference curves
- The farther an isoquant from the origin, the greater the level of output
- Isoquants don’t cross
- Isoquants slope downwards
- Isoquants must be thin
What is the assumption of efficient production underlying production functions?
The assumption underlying a production function is that it represents efficient production. This means it assumes the most effective use of inputs to produce the maximum possible output. It implies that resources are utilized optimally, and there is no waste in the production process. The production function reflects the ideal relationship between inputs and outputs when the production process is operating efficiently.
What’s an important difference between isoquants and indifference curves?
Isoquants have cardinal proportions and not just ordinal ones
What does the curvature of isoquants indicate?
The shape of isoquants indiciates how easily a firm can substitute between inputs
What are the types of isoquants?
Perfect substitutes
Fixed proportions
Convex
Draw me a perfect substitute isoquant
Draw me a fixed proportions isoquant
Draw me a convex isoquant
“Isoquant for the production function”
What does the slope of an isoquant show?
The ability of a firm to replace one input with another (holding output constant)
What is the Marginal rate of technical substitution MRTS?
The slope of an isoquant at a single point
What is formula for MRTS
Change in capital/change in labour
dK/dL
As we move down and to the right along an isoquant
Increase L - output up by MP(L) * dL
Decrease K - output down by MP(k) * dK
Output is constant so
MP(L) *dL + MP(k) * dK = 0 thus,
MRTS = -MP(L)/MP(K)
What do convex isoquants exhibit?
A diminishing marginal rate of technical substitution
What is a diminishing marginal rate of technical substitution?
The more labour the firm has, the harder it is to replace remaining capital with labour
As we move down the isoquant what happens to MRTS?
MP(L) goes down and MP(K) goes up
So MRTS = -MP(L)/MP(K) gets closer to 0
Isoquants and the DMRTS is similar to what?
Indifference curves and marginal rate of substitution between goods and
What causes movement along an isoquant?
Increasing one input while decreasing the other by an offsetting amount
How to move to higher isoquants
Increase one input while holding the other consyant
What does a production function exhibit when a % increase in inputs is followed by the same percentage increase in output?
Constant returns to scale
Doubling inputs does what?
Double output
q = f(2L, 2K) = 2f(L,K)
What does a production function exhibit when a percentage increase in inputs is followed by a smaller percentage in output
Decreasing returns to scale
Why does decreasing returns to scale often occur?
Difficulties with organising and coordinating activities as firm size increases
What is typical in terms of returns to scale in many production functions?
Many production functions exhibit varying returns to scale as output increases
Consider a Cobb Douglas production function. What does the power a+b tell us?
If a+b=1 output doubles so CRS
if a+b<1 output less than doubles so DRS
if a+b>1 output more than doubles so IRS
What is the typical pattern for production functions (returns to scale) as output increases?
- Increasing return to scale at low levels of output:
a small firm can gain from greater specialisation of workers and equipment by growing larger
- Decreasing return to scale at higher levels of output: organising, and coordinating activities, becomes more and more difficult as firm increases 
What do firms do?
Convert inputs to outpurs
What does a production function show?
Relationship between inputs and outputs when production is efficient
What is an isoquant?
An isoquant shows the input combinations that produce a specific level of output.
Almost like a map that shows all the different combinations of inputs with different levels of each input to produce a certain. Output.
What does the MRTS show?
Slope of isoquant. Shows substitutability of inputs.
Shows how much of one input can be replaced by another without changing the level of output.
How to calculate APL + MPL?
APL = divide by Labour (L)
MPL = derive with respect to Labour (L)
