Lecture 15 - Production functions Flashcards
What is a firm?
A firm is an organisation that converts inputs (labour, materials and capital) into outputs
Define capital services (K)
Capital services (K) includes the use of long-lived inputs such as land, buildings and equipment
Define labour services (L)
Labour services (L) includes the hours of work provided by managers and workers
Define materials (M)
Materials (M) includes natural resources and processed products consumed in producing, or incorporated in the final product
What must a firm do to maximise profits?
- To maximise profits, a firm must produce efficiently
- A firm produces efficiently if it cannot produce more output for a given quantity of inputs
How integral is efficient production in order to maximise profits?
Efficient production is a necessary condition for profit maximisation but not a sufficient condition
What is a production function?
- A production function summarises the various ways that a firm can efficiently transform inputs into outputs
- The production function shows only the maximum amount of output that can be produced from a given combination of inputs
Assuming that labour (L) and capital (K) are the only inputs, what is the production function?
The production function is q = f(L,K)
What is the short run?
The short run is a period of time so brief that at least one factor of production is fixed
What is the long run?
The long run is a period of time long enough that all factors of production are variable
What do we assume about capital and labour in the short run?
We assume that in the short run capital is a fixed input and labour is a variable input
State the short run production function
- The short run production function is given by:
q = f(L,Ꝁ) - This shows that in the short run capital is fixed
What does the symbol q represent in production functions?
- q represents output which is also called the total product of labour
- The total product of labour is the amount of output (total product) that a given amount of labour can produce holding the quantity of other inputs fixed
What is the marginal product of labour?
The marginal product of labour is the additional output produced by an additional unit of labour, holding all other factors constant
How do we calculate the marginal product of labour?
- We get the marginal product of labour by differentiating the production function with respect to L
- MPL = dq/dL
What is the average product of labour and how do we calculate it?
- The average product of labour is the ratio of output to the amount of labour employed
- APL = q/L
State the law of diminishing marginal returns
- The law of diminishing marginal returns states that if a firm keeps increasing an input whilst holding all other inputs and technology constant, the corresponding increases in output will eventually become smaller
- Mathematically, this occurs when MPL<0
In an economy, if there are just two inputs of capital and labour, what is the production function?
- q = f(L,K)
- This means that the production function is some function of L and K
What is an isoquant?
An 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:
1- The further an isoquant is from the origin, the greater the level of output
2- Isoquants do not cross
3- Isoquants slope downwards
4- Isoquants must be thin
What is the main difference between indifference curves and isoquants?
Isoquants have cardinal properties as well as ordinal ones whereas indifference curves only have ordinal properties
What does the shape (curvature) of an isoquant indicate?
The shape (curvature) of isoquants indicate how easily a firm can substitute between inputs
Draw the general isoquants for perfect substitutes, fixed-proportions and convex
See slide 16 of lecture 15
What does the gradient/slope of an isoquant tell us?
The gradient/slope of an isoquant shows the ability of a firm to replace one input with another (holding output constant)
What is the marginal rate of technical substitution (MRTS)?
The marginal rate of technical substitution (MRTS) is the gradient/slope of an isoquant at a single point
State the formula for calculating the MRTS
MRTS = Change in capital/Change in labour = -MPL/MPK
What do convex isoquants exhibit?
Convex isoquants exhibit a diminishing marginal rate of technical substitution
What does moving to higher isoquants and movement along isoquants represent?
- Moving to higher isoquants represents increasing one input while holding the other constant
- Movement along an isoquant represents increasing one input while decreasing the other by an offsetting amount
When does a production function exhibit constant returns to scale?
- A production function exhibits constant returns to scale when a percentage increase in inputs is followed by the same percentage increase in outputs
- For example, doubling inputs doubles output
Do linear production functions have constant returns to scale eg. q =K+L
Yes, linear production functions do have constant returns to scale
When does a production function exhibit increasing returns to scale?
A production function exhibits increasing returns to scale when a percentage increase in inputs is followed by a larger percentage increase in output
When does a production function exhibit decreasing returns to scale?
A production function exhibits decreasing returns to scale when a percentage increase in inputs is followed by a smaller percentage increase in output
What is the general form of a Cobb-Douglas production function?
A Cobb-Douglas production function has the general form: q = AL^aK^b
What is the general pattern of returns to scale?
- There is typically increasing returns to scale at low levels of output as small firms can gain from greater specialisation of workers and equipment by growing larger
- There is typically decreasing returns to scale at higher levels of output as organising and coordinating activities becomes more and more difficult as firm size increases
How does the spacing of isoquants reflect different returns to scale?
- The closer the isoquants are together, there is increasing returns to scale
- At medium separation of isoquants, there is constant returns to scale
- At large separations of isoquants, there is decreasing returns to scale
