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Optimal Scale and X-Inefficiency

Considerable knowledge (aka perfect information) is required to understand/calculate the optimal technical output for a firm, but it must be understood so that a firm can make the best decisions regarding production. It must be noted that sometimes it is not possible for a firm to actually produce on the ‘optimal technical efficiency’ because there is simply not enough demand.

The X-Inefficiency is also known as the ‘production cost gap’ and is found in companies that are producing the maximum output, but are not producing at the optimum technical efficiency. There are several reasons this may occur:

  1. the firm is not producing at the optimal scale of production.
  2. the firm does not function efficiently and wastes resources.

It can be seen from the diagram above that there are several points of interest. These include:

  • X’ is the point where maximum output is reached but the cost of production is too high, as it does not sit in the Average Total Cost Curve.
  • the vertical distance between X’ and the ATC Curve is the X-Inefficiency.
  • X is a poor position for a firm to be producing at, as the cost of production is high (above the ATC Curve) and output is low. This firm would be in danger and would require restructuring.

Production jargon & relationships between cost and output

Long and Short Run are terms that can be confusing from an economics perspective, as they are not based on a time dimension.

The Short Run is a period where at least one input is fixed (eg personell employed), and this is also known as the operating period.

The Long Run is a period where are inputs are seen to vary, and is also known as the planning horizon. 

Diminishing Returns of Production

ASsuming that the firm is using all existing resources efficiently, then the extent to which the firm can alter its output depends on the extent to which the firm can vary its inputs.

The Law of Diminishing (Marginal) Returns

In the short run, when one or more factors are held fixed, there will come a point beyond which the additional output from using extra units of the variable inputs will diminish.

There will be an output beyond which the addition of units of variable factors such as labour, against a fixed input such as capital will result in a decline in output per employee. This is known as the Average Physical Product of labour.

Marginal Physical Product

This is the change in total output seen from employing each additional unit of variable factor input.

The Relationship between Production and Costs

The output at which the average cost per unit is at its lowest is known as the Technically Optimum Output.

The change seen in total costs of production as output is changed incrementally is referred to as the marginal cost. Where the total cost curve is linear, the marginal cost is constant, and it is easier to refer to this as the marginal cost of output.

The Incremental cost per unit is the total change in costs caused by the output increment. in other words  the incremental cost equals the average marginal cost over the range of outputs.

Classification of Profits

Normal profits are made when profits ‘just’ cover the opportunity cost of investing this capital elsewhere. It is the minimum level of profits required for a firm to continue trading.

In incorporated companies this is equal to the ‘cost of capital’, which would include interest on loans and returns to investors.

In non-corporate entities this is the amount of profit required to persuade investors to invest money into a company to undertake production risks in an industry.

Supernormal Profit is seen to be all profit made above this normal profit.

The Analysis of Production Costs

The Production Function

There are several things to be considered when deciding upon methods of production. These include:

  1. Technical Efficiency – this is related to engineering considerations and labour skills etc.
  2. Relative Prices of factor inputs.

We will assume that managers wish to minimise costs of production, and thus maximise profit. This is not always possible in reality due to factors such as labour union agreements on the size of workforces etc.

The production function is a mathematical expression to relate the quantity of all inputs to the quantity of outputs, assuming managers employ all inputs efficiently. It may be expresses as follows:

Q = F(I1, I2, I3, I4…..In)

The inputs are usually classified under 3 categories. These are:

  1. labour.
  2. capital.
  3. land.

The Cost Function

The cost function is important for maximising profit, so that cost of output can be seen next to cost of inputs used.

C = F(Q, p1, p2, p3….pn).

Variable Costs vs Fixed Costs

Fixed Costs are those costs that do not vary as output changes. These might very well include; office rent, machinery (to the point where more machines are required for further increases in production).

Variable Costs are those costs that do alter as output changes, and these will include things such as; fuel, energy consumption, raw materials, staffing levels.

Total Costs of Production =  total fixed costs + total variable costs

TCP = TFC + TVC

If we were to average values over TFC and TVC we can derive values for Average Fixed Cost and Average Variable Cost.

Points to note:

  • Total fixed costs remain constant for all levels of output.
  • Total variable cost, and therefore total costs rise as output increases.
  • Average fixed costs decline as output increases, as the fixed costs are distributed over more and more output.
  • Average Variable Costs may fall initially, but will level off and even rise after a certain output due to the Law of Diminishing Marginal Returns.
  • Average Total Costs (ATC) = AFC + AVC, tend to decline initially and then rise after a certain output level (Q) is reached. ATC is often referred to by accountants as the unit cost, and also the average cost.

Therefore:

TC = TFC + TVC
AVC = TVC/Q
AFC = TFC/Q
TF = AFC + AVC = TC/Q

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June 2017
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