Svend Rasmussen

Estimating the Technical Optimal Scale of Production in Danish Agriculture

Abstract This paper uses representative farm account data for 1985–2007 to estimate stochastic production frontiers in the form of input distance functions for Danish crop, dairy and pig farms. The objective is to study and compare scale economies for the three farm types. The estimated technical efficiency is relatively constant over time for all three farm types, but the elasticity of scale differs. Although the size of all farm types has increased considerably during the last 20 years, more than 95% of the crop farms and 85% of the dairy and pig farms are still below the estimated technical optimal scale of production. The results support the hypothesis that the restrictions concerning the amalgamation of farms and the purchase of farm land have seriously prevented Danish farmers, and especially cash crop farmers, from taking full advantage of scale economies.

Use of Linear Programming in Practical Production Planning

This chapter discusses how the linear programming model can be used as the basis for a company’s operational planning, in practice. The presentation and construction of the LP models will be accounted for through the use of simple examples, primarily from agriculture, and the discussion is aimed at finding a combination of the presented techniques and methods that can then be used to outline a model for the total planning of an agricultural operation. Although the examples are from agriculture, the modelling technique is applicable in other industries.

Risk and Uncertainty

Closely linked with the problems associated with the timing of production, as discussed in the last chapter, is risk and uncertainty, which are often associated with the production and sale of products. Implementation of production that takes a very long time is often associated with uncertainty regarding the price which can be obtained for the product by selling at a later date. When it comes to bio-based production such as agricultural crops and other agricultural products, there is also uncertainty as to the production yield, since climatic conditions and diseases may play a role.

Production Over Time

Time is a key input in all kinds of production. However, the subject of using time for production is more relevant in some industries than in others. The distinguishing feature of agriculture and other biologically based industries compared to other industries is the fact that production often takes quite a long time. Just think of the production of wood from beech trees, which first reach maturity after 50–100 years of growth!

Modelling Supply Functions Using Linear Programming

This last chapter provides an example of how to integrate the production economic theory presented in the first ten chapters of this book and the Linear Programming approach presented in the last three chapters. The example shows how is it possible to use Linear Programming to numerically generate the output supply function of the firm. This approach has shown to be a suitable modelling unit in a sector modelling context, in which the supplies from the individual firms are aggregated into the total industry supply.

Optimisation with One Input

This chapter discusses the optimisation of production under the simplest preconditions: The production of one product (output) using one input. The amount of the other inputs is presumed given as fixed amounts. The prices of inputs and outputs are presumed given externally (the producer is a price taker) and these prices are presumed to be constant, no matter how much the producer buys and sells.

Economies of Scale and Size

The two concepts economies of scale and economies of size describe what happens to production or costs when the size of the firm changes (increases). Economies of scale describe how much production increases when the firm increases its scale of production, i.e. increases all (both fixed and variable) inputs by a common proportionality factor. Economies of size describe what happens to cost per unit of output when production increases in a cost minimising way.

The Linear Programming Model

The linear programming model which is described in the following is based on a special type of production function, the so-called Leontief production function.

Decreasing Sales Curve

The discussion so far has been based on the assumption of perfect competition in the product market – where the producer is a price taker, i.e. can sell unlimited amounts at one and the same price.

Productivity, Efficiency and Technological Changes

The description of the production within an industry is often based on empirical data. In Denmark, there is an abundance of data for the description of production within farming. On the micro-economic level, this would be, for example, notes and financial accounts from the individual farms, and on an industry level it would be various kinds of statistical information describing production, factor consumption, prices etc.