Production Economics

Frontmatter

Chapter 1. Introduction

Abstract

This book is concerned with production and related economic issues.

Generally speaking, production consists of the transformation of factors of production into products. The way in which the production is carried out—the production process—is outlined in Fig. 1.1.

First, the factors of production (also called input) are taken to a production plant, which is where the actual production is carried out by way of a production process, the result of which being one or more products (also called output).

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Chapter 2. The Production Function

Abstract

Economic theory is, to a large extent, about money—about costs, prices, markets, return on investment, profit and similar economic concepts. This is also the case for the theory of production economics. However, the theory of production economics is special in that the limits of economic behaviour are defined by the technical production possibilities. Production technology is the decisive factor regarding the quantity produced and how it may be produced. Therefore, a very important part of the theory of production economics consists of describing the production technology which defines the framework for the economic behaviour.

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Chapter 3. Optimisation with One Input

Abstract

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.

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Chapter 4. Production and Optimisation with Two or More Inputs

Abstract

In the real world, no production is carried out using only one input. Normally, several (controllable) inputs are used. Hence, when growing cereal crops, land, seeds, labour, fertiliser, pesticides, machinery, etc. are used. A car manufacturer uses steel, labour, leather, plastic, paint, tyres, fuel, etc. Various inputs can often replace each other so that it is possible to replace some of the expensive ones with cheaper alternatives if the price of one input increases. For example, if the price of pesticides, which are used to chemically control weeds in the field, rises, then the use of labour might be considered as an alternative to control the weeds. If the price of fuel used for heating factory or office buildings increases, it may be cheaper to use electricity for heating instead. The question as to the extent to which the various inputs can replace each other becomes the key question in this connection. This chapter deals with the instruments which can be used to address such issues. As in Chap. 3, we assume competitive input and output markets.

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Chapter 5. Costs

Abstract

Costs are the monetary value of input used over a period of time. A company’s costs can be derived from the production function. The point of reference is a production function with one variable input x ₁ and an output y, as shown in the left hand side of Fig. 5.1. If you imagine this figure removed from the paper, lifted up, and then put down again with the front side down and turned 90° clockwise, then you will get the figure—the cost function—in the right hand side of Fig. 5.1. The curve in the right hand side of Fig. 5.1 is not, of course, an entirely correct cost function. Costs are measured in monetary terms (MU), and the unit of measurement on the vertical axis on the figure in the right hand side is not MU, but units of input x ₁. However, if the units on the vertical axis are multiplied by the price w ₁ of x ₁, and if x ₁ is furthermore measured in units having the exact price of w ₁ = 1, then the figure to the right does in fact measure the variable costs (VC(y) = w ₁ x ₁(y)) as a function of the production y, as the applied input amount x ₁ is rendered as a function of the production y.

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Chapter 6. Productivity, Efficiency and Technological Changes

Abstract

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.

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Chapter 7. Input Demand Functions

Abstract

In this chapter, the theory introduced in Chap. 4 will be used to derive the company’s demand for input used in production. Furthermore, how the theory can be used to analyse what happens to the demand for input when the relative prices vary will also be examined. The representation in the first sections of this chapter presupposes a market with perfect competition, i.e. the company is a price taker and does not have the possibility of influencing the market price for the required inputs. At the end of the chapter (Sect. 7.5), the input demand under the more general assumption that the price for input can vary, depending on the amount demanded by the company, is discussed.

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Chapter 8. Land and Other Inputs

Abstract

In the previous chapters we derived conditions for a cost minimising combination of inputs (Chap. 4), and studied how the demand for variable input depends—not only on the input price, but also on the prices of other variable inputs that may be used to substitute the input in question (Chap. 7). However, there are special cases/inputs when it is not possible to apply the previous models directly, and the concept of the pseudo scale line becomes useful.

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Chapter 9. The Company’s Supply Function

Abstract

As described in Chap. 4, the company maximises its profit (profit maximisation) if production is expanded to the point where the marginal cost (i.e. the incremental cost of producing one more unit) is precisely equal to the product price. The product price is in fact equal to the additional revenue achieved from selling one more product unit. The criterion for profit maximisation can therefore also be expressed as the point where the marginal cost is equal to the marginal revenue.

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Chapter 10. Optimisation of Production Under Restrictions

Abstract

The general criteria for the adjustment of production when product and factor prices change were described in Chap. 3–5. The general results are derived under the general assumption that the producers wish to maximise profit. The general criterion for profit maximisation is that the addition of input should be continued as long as the increase in total revenue (i.e. marginal revenue) is greater than the increase in costs (i.e. marginal costs). This general criterion includes the following two criteria as special cases: (1) The value of the marginal product for all (variable) inputs must be equal to the price of the corresponding input (VMP _i  = w _i ), and (2) The marginal costs must be equal to the price of output (MC = p _y ).

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Chapter 11. Economies of Scale and Size

Abstract

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.

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Chapter 12. The Fixation of the Production Factors

Abstract

Fixed production factors have previously been defined as being production factors the quantity of which cannot vary within the planning horizon under consideration. Hence, they are characterised by the fact that the company is unable/unwilling to buy or sell production factor units.

However, how are these fixed production factors “generated”? What is the reason why some production factors are fixed whilst others are variable? For how long is a production factor actually fixed? And what is the financial implication of some production factors being fixed? As such, fixed production factors are supposed to entail restrictions which we would like to avoid.

It is questions like these that will be discussed in this chapter. In this connection, there will be a particular focus on the description of the ways in which the fixation of production factors affects the economic behaviour of the producers.

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Chapter 13. Decreasing Sales Curve

Abstract

The discussion so far has been based on the assumption of perfect competition in the product market—whereby the producer is a price taker, i.e. can sell unlimited amounts at one and the same price. While this precondition is realistic in connection with small companies producing standard goods within an industry such as farming, the precondition becomes problematic in connection with larger producers, or producers producing differentiated products/special products for a smaller segment of the market. This could in fact also be problematic for producers who, for some reason or other, have achieved a position whereby they are the only producers of a specific product and have therefore attained a monopoly position in the market. For such producers, the assumption that it is possible to sell any amounts at the same price is of course invalid. The company’s sales curve is, under such conditions, equal to the market demand curve (D), which is normally a falling curve as illustrated in Fig. 13.1.

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Chapter 14. Production Over Time

Abstract

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!

How is the time consumption optimised in a production process? What is the decisive factor for determining when to send an animal, e.g. a slaughter pig or a beef calf, to the slaughterhouse? Should it be sent to the slaughter house one week earlier or later? What is the decisive factor for how many years the strawberry plants should be used before removing and replacing them with other plants? How much time should pass before a stand of trees is felled so that new trees can be planted? It is issues like these that will be discussed in this chapter.

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Chapter 15. Risk and Uncertainty

Abstract

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.

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Chapter 16. Economic Rent and the Value of Land

Abstract

The concept of fixed production factors was introduced and discussed in Chap. 12. The main result is that production factors become fixed when it does not pay for the firm to buy more, because the purchase price is higher and the sales price is lower than the internal value of the production factor to the firm. The larger the difference is between purchase and sales price, the higher the probability that a production factor will become a fixed factor.

A production factor earning revenues which are higher than the costs needed to keep it in the present employment is said to earn economic rent. The formal definition of economic rent is that it is those payments to a production factor that are in excess of the minimum payment necessary to keep it in the present employment. Alternatively, one can define economic rent as being those payments that are in excess of the minimum payment necessary to have the factor supplied.

According to the definition, all fixed factors earn some economic rent. However, the original meaning of the concept (pure economic rent) is derived from rare and valuable qualities of nature/natural resources such as a rich and productive vineyard, a piece of land where there are raw materials such as oil, copper or gold, a building site with a view of the sea, or a piece of productive agricultural land. The common characteristic is that these factors are unique in the sense that they cannot be reproduced and that they are only available in a certain amount.

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Chapter 17. Production of Multiple Products

Abstract

A company often produces several products, which gives rise to new issues compared to the situation in which only one product is being produced. If, for example, there are limited amounts of input at disposal, then how this input should be allocated between the various products needs to be decided. Multiple products can also give rise to economic issues concerning production in another way. It may be the case that the production of the multiple products results in advantages, e.g. a kind of synergy. Producing two products at the same company can also give rise to advantages regarding cost savings when compared to separate production.

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Chapter 18. The Linear Programming Model

Abstract

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.

The Leontief production function is different from the general neoclassical production function in that it consists of straight lines and the isoquants are L-shaped, indicating that it is not possible to substitute between input factors, and that the input factors, therefore, are used at a fixed ratio.

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Chapter 19. Production Planning in the Linear Programming Model: Linear Programming

Abstract

This chapter discusses how the linear programming model that was introduced in Chap. 18 can be used as a basis for production planning. Using the concepts already described in Chap. 18, the production planning problem can be briefly defined as the act of determining the value of the intensity vector x which is used to maximise the company’s total financial result, i.e. whereby c is a [n × 1] vector of the financial results of the unit processes, and x is a [n × 1] vector of intensities for the possible production processes. As can be seen, (19.1) is a linear function with no maximum (the c _i ’s are presumed to be >0). The production planning problem is, therefore, only relevant if the company’s production is subject to certain restrictions. In the short and medium run, the production will be restricted by the quantity of fixed input factors available to the company. The maximisation in (19.1) must thus be carried out under the constraint that the consumption of the input does not exceed the available quantity.

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Chapter 20. Use of Linear Programming in Practical Production Planning

Abstract

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.

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Backmatter