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Least-cost solution

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  • Category: Economics

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The term least-cost solution does not describe one specific principle in economics. Least-cost solution covers a wide diversity of economical topics that help form an ultimate solution.

The term can be introduced in the context of a firms aim and objectives e.g. “profit maximization”. In many cases firms may have other objectives such as providing quality to customers and thus may adopt techniques such as total quality management (TQM). Organizations such as Banks often prefer to focus on providing efficient services. Occasionally firms abide by aims and objectives other than profit maximization to encourage and enhanced operational techniques and image.

Ultimately most firms override aims to concentrate on maximizing profits. At this point a firm will operate accordingly to reduce costs and maximize return in order to acquire full financial benefit from the output. When a firm adopts such an aim it is categorized as the usual theory of supply, hence is also known as “theory of the firm”.

A firm calculates its profits by subtracting the total costs of production from the total revenue generated from the sales of that produced amount. (See Figure 1)

Figure 1


Profit = Total Revenue ¡V Total Costs

Total Income from Sales Variable Costs + Fixed Costs

Firms must first eliminate unnecessary costs and increase sales performance to generate maximum profit. The firm should minimize costs that do not have a direct influence on sales and output.

A firms inputs and their expenditure (Factors of Production) have a strong influence on the cost of a firms output. If a firm increases its production due to a rapid increase in demand, there may be a delay in acquiring the necessary inputs/resources. For example a firm can employ more labour to manufacture more produce. However due to a limiting factor such as machinery and land storage space. The firm may not be able to increase its output therefore employing additional workers will result in an opportunity cost. In turn this increased cost will inversely affect the profits of the organization.

From this we can devise the meaning of fixed and variable factors. A fixed factor is an input that cannot be increased within a given time period (e.g. land and machinery). A variable factor is one that can be fluctuate over a given time period (e.g. Labour). Once we understand these concepts we can begin to distinguish between short run and long run.

The short run is where at least one factor remains fixed over a period of time, in which case output can be increased using more variables. For example an airline company may want to carry more passengers. It can increase staffing and the amount of journeys made. However it cannot buy or build another aeroplane in a short period. The long run is a time period that is long enough to allow for all inputs to be varied. For example in the long run a firm may be able to build more machines and buy more land for storage.

The term “least-cost solution” is used by firms who wish solely to profit maximize. The solution devises a technique of production which designates a point that keeps costs at its least to keep profits at their greatest. In the long run all factors can be varied and a firm can alter and decide on which technique of production to implement. Conversely the predicament occurs when a firm needs to decide on how the technique should be formulated and how the most advantageous factors of production are chosen?

A firm therefore combines factors at a point of “least-cost” to produce the desired output and form a solution (technique) where all variables work towards achieving maximum profit.

In the long run where there are two variables (capital (K) and labour (L). The least cost solution of the two would be where MMPL/PL = MMPK/PK i.e. where the last pound spent on each factor and the extra product (MMP) is equal. At this point substituting one factor for another can make no further gain. The firm’s productive efficiency when operating on a least-cost solution is likely to be at its peak. Each factor is proportionally utilized at its best.

MMPL/PL > MMPK/PK at this point there is more amount of labour than capital. The firm will be receiving a greater physical return from its workers than from extra capital. In these circumstances the law of diminishing return is applied. The law states that when an increased amount of a variable factor is used on a fixed factor, it will eventually reach a stage where every unit thereafter will produce less than the previous unit.

Figure 2

Figure 2 above shows an isoquant. This diagram can be used to help better understand and graphically represent the least-cost solution. The diagram indicates points where the output will remain constant regardless of the units of capital or number of workers. These points are joined to form the isoquant. At any point along the isoquant output will remain the same. For example the given diagram shows a firm with a maximum output of 4000 units. All points from a-d will have different proportions of the two variables. Point represents a more capital-intensive technique whereas point d is more labour intensive. We can see from the diagram that the isoquant must slope negatively, or be convex to the origin, in order to be efficient and effective.

At a point where capital is fixed, in order to increase the output (Q2) when labour increases, point d uses more labour than point c. However if labour was to increase further the isoquant line Q1 is applied. This is because point f uses more labour than point e. It is therefore visible if one output is fixed. We also know that output cannot be increased indefinitely.

Figure 3

The isoquant must be convexed to the origin; this illustrates the diminishing marginal rate of factor substitution (MRS) in relation to the law of diminishing return. See fig 3.

The MRS is the amount of one factor (e.g. K) that can be replaced by a 1 unit increase in the other factor (e.g. L). Therefore if 2 units of capital could replace one unit of labour then the MRS would be 2. The MRS between two points on the isoquant will equal the slope of the line joining those two points. Figure 4 shows the MRS between points g and h is 2.

Figure 4

The levels of output can be determined using an isocost. Assuming that price is a fixed factor, we can construct the isoquant. We an define an isocost as being a line showing all the possible combinations of two factors that cost the same to employ.

The isocost line (see Figure 5) helps firms solve which least cost technique of production is to produce a specific level of output. In order to find the least-cost combination factors to produce a certain level of output, the isoquant must be drawn as in Figure 6. The least cost solution is at point x as it is the point where the isoquant just touches the lowest possible isocost as a tangent.

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