The Producer Theory is somewhat parallel to the Consumer Theory in terms of the concepts describing producer behaviour. Just like how consumers seek to maximise their utility, producers are concerned with profit maximisation.
- Profit = Revenue – Cost
To maximise profit, it is essential for producers to achieve efficient production. Meaning regardless of the quantity that the firm would like to produce, production costs is minimised to the lowest possible.
The production function relates the factors of production to the quantity of goods produced. This function behaves similarly to the consumer utility function.
- Quantity produced, q = function of ( Labour L, Capital K )
There are two factors of production, which is labour (L) and capital (K), the latter includes everything else required for production, such as land, plants, machines and etc.
Another concept relating to factors of production is the distinction between variable and fixed inputs. Variable inputs can be easily changed while fixed inputs cannot. In order to simplify our analysis, we assume that there are two time horizons. In the Short Run (SR), capital is fixed but labour is variable. To improve efficiency, producers will adjust labour input. In the Long Run (LR), both capital and labour can be adjusted to improve production efficiency. The intuition to understanding this is that capital, such as factories, take a longer time to build, as compared to workers, which can be employed in a much shorter time.
Decision making in the Short Run
Firms will be looking at the Marginal Product of Labour (MPL) to decide the optimal input of labour, and hence minimal labour cost, for any quantity of production required. MPL is the contribution to the quantity of goods produced by the last additional unit of labour input. A key characteristic of this marginal analysis is the Diminishing Marginal Product of Labour: each additional unit of labour contributes less to the quantity produced. Intuitively, this is the natural consequence of a fixed capital input, which ultimately limits production.
Decision making in the Long Run
As both labour and capital are variables, isoquants (isometric quantities) can be plotted to reflect the long run production process.
Isoquants reflect the different combinations of labour and capital inputs that produce the same quantity of goods (this is parallel to consumer preference map). The gradient of the curve reflects the Marginal Rate of Technical Substitution (MRTS) between labour and capital. As seen from the diagram, MRTS is different along the curve. Intuitively, at a point of production which is labour-intensive, an additional unit of capital input is much more productive than an additional unit of labour, and vice-versa for a production point that is capital intensive.
In a scenario which labour and capital are perfect substitutes, the isoquants will be linear, as MRTS is constant. The production function may take the form of q = L + K.
In the other extreme, where labour and capital are non-substitutes, the isoquants will be L shaped. Additional unit of either inputs is not going to increase production. The production function may take the form of q = min( L , K ). These are also known as Leontief production functions.
Returns to Scale
This is the concept of how production increases as input increases. In a case of constant returns to scale, the production increase proportionally to the increase in inputs. Mathematically:
- func( 2L , 2K ) = 2 * func( L , K ) = 2q
In the case of increasing returns to scale, the production increases much more than the increase in inputs. This can be due to specialisation and technological benefits from producing at a larger scale. Mathematically:
- func( 2L , 2K ) > 2 * func( L , K )
In the case of decreasing returns to scale, the production increases less than the proportion of inputs increased. This is because the scale of production inputs had already reached the saturation point, and any further increase in inputs is not going to yield much more benefit. Mathematically:
- func( 2L , 2K ) < 2 * func( L , K )
Productivity also affects production, and it can be used to explain why production increases over time with the same combination of input unchanged. Productivity is dependent on technology and processes. To include productivity into the picture, the production function can be rewritten as:
- quantity produced q = productivity (A) * func( L , K )
Cost of Production
Knowing how inputs affects quantity of production is insufficient to maximise profit. Producers will have to use that knowledge to minimise cost. The variety of terms related to cost are as follows:
- Fixed Cost (FC) = cost that cannot be changed in the short run. Eg. rental for plants and machines.
- Variable Cost (VC) = cost that can be changed in the short run Eg. labour
- Total Cost (TC) = FC + VC
- Marginal Cost (MC) = the additional cost incurred for the last additional unit of goods produced. Mathematically, it is the change in cost / change in quantity produced.
- Average Total Cost (ATC) = total cost / total quantity produced.
- Sunk Cost = are fixed forever and can not be changed. Eg. medical qualification of doctors in a hospital. The investment to acquire their skills is a sunk cost that will never vary in future.
Upward Sloping MC
In the short run, MC will be the change in labour cost over the change in quantity produced, or mathematically:
- MC = W / MPL
As wage W is constant, this shows that marginal cost is increasing due to diminishing marginal product of labour. It is increasingly more expensive as each additional labour produces less goods. Therefore in the short run, cost minimisation is limited as quantity of goods produced is directly contributed by labour inputs, which is always upward sloping in marginal cost.
Long Run Cost Minimisation
In the long run, to achieve profit maximisation, producers need to achieve optimal production (producing somewhere on the isoquant) at the lowest cost (cheapest point of the isoquant).
Isocost lines map the points of production for various combinations of labour and capital that sum up to the same cost of production. Therefore, the optimal point of production for a desired quantity goods can be found at the tangent of the isocost line and the isoquant of that quantity of production. This is parallel to consumer budget constraint meeting preference map.
Whenever there is a change in wages of labour or rental of capital, the gradient of isocosts will change, and a new optimal point of production will be established at the new tangent to the same isoquant.
A long run expansion path can be obtained by mapping all optimal points of production for all levels of quantity of production. The path shows the optimal adjustments to input when producers decide to change the quantity of production. The gradient of the path will indicate in the long run whether labour or capital increments have a greater impact on production.
How much to produce?
The production theory does not determine the quantity of production as this is a decision that the firms will have to make based on the market competition. This theory merely point out the optimal means of production that is aimed at maximising profit, for a desired quantity of goods.
(Reference: MIT OCW Principles of Microeconomics)