Fixed costs are incurred irrespective of whether or not production is undertaken. Thus, they do not change in magnitude depending on the amount of output produced. Examples of fixed costs include land taxes, principal and interest payments on loans, insurance premiums, wages for permanent employees.
These are cash costs. Non-cash fixed costs include depreciation costs on buildings, machinery and other equipment, interest charges on capital investments and charges on family labor and management. Variable costs depend on the level of production.
They include purchased inputs such as seed, fertilizer, herbicides, insecticides and hired labor. In the case of livestock within a single production season, feed and medicine are the major variable cost items. Total Costs 1. Total fixed costs TFC represent the summation of all the fixed costs. This is constant throughout the production process for a given period. Total variable costs TVC are computed by multiplying the amount of variable input used by the price of per unit input.
These costs vary as output changes. From these basic cost functions, a number of other cost functions can be derived as presented below:. This effect is due to spreading fixed costs over more output. The AVC varies depending on the level of production. The level of the AVC curve depends on the unit cost of the variable input.
For a production function the APP measures the efficiency of using variable inputs, likewise in the case of cost functions, the AVC provides the same measure. That is, the cost of producing one unit of output.
As the level of production increases from zero, the ATC initially declines due to spreading fixed costs among an increasing number of units of output. Also due to increasing efficiency in using the variable inputs as indicated by a declining average variable cost curve. However, as output increases further, AVC attains a minimum and it begins to increase. The marginal cost is defined as the change in total cost, per unit change in output. It is the cost of producing one additional unit of output.
From an economic point of view, at this point the MC ceases to have any meaning. Rather, this is referred to as the marginal factor cost MFC. These various cost functions can also be represented in tabular form as shown in Table 3.
As part of the class exercise, fill in the remaining gaps in table 3. Thus, costs are usually expressed as a function of output. It is the increase in total cost resulting from one unit increase in output.
NOTE that the marginal cost is not the change in Total cost given a unit increase in inputs. Direct estimation of cost functions involves making estimation of costs and output at various levels of production for a given technology. This can be attained using cross sectional data from a sample of firms eg.
Farms that are involved in a given production process. Also data for direct estimation of cost functions may be obtained from time series data for a particular firm over time. In such a case, the firm must have changed the volume of production over time, using different levels of inputs.
Direct estimation of cost function therefore entails statistical analysis of accounting data together with engineering or production data to derive appropriate cost functions. Other cost functions may be derived as previously defined. Senkondo made direct estimation on the Total cost function using production and accounting data from Kilombero Sugar Company as follows;.
For another example of a case where the cost function is known, see Doll and Orazem Chapter 2. Cost curves express the cost of fixed and variable inputs, as functions of the amount of output.
Meanwhile, production functions express output as a function of inputs. But input costs are the product of input quantity times the input price. It follows therefore that cost and production functions must be inversely related. This means, knowledge of one implies knowledge of the other, as long as input prices are known. Normally, cost functions are expressed as a function of output rather than input.
In order to meet this requirement, we express the inputs as a function of output. This is the inverse production function represented as follows:. This inverse function does not imply cause and effect. In other words, the function above does not imply that output Y causes input X. Rather, the inverse equation f-1 is a. The main assumption for profit maximization is that farmers by their inputs in purely competitive markets.
It is likewise assumed that they sell their products in competitive markets. This means as buyers, the volume of their purchase is too small to influence the market price, also, the volume of their sale is too small to change the market price.
Students should review theories of monopoly, oligopoly, perfect competitive markets etc and write brief notes on each type of market. Listed below are main characteristics that differentiate markets. The agricultural industry in Tanzania may be cited as one example whose characteristics make it close to a competitive market. Thus Prices are assumed to be constant at a given point in time. Before we proceed, we need to make additional assumptions about farmers and the market conditions under which they operate.
In a purely competitive market individual sellers are assumed to be price takers, which means the quantity of a product supplied by one farmer to the market does not change the price a given point in time. Thus for the purpose of decision making, the product price is assumed to be constant for the individual farmer, the TVP function has the same shape as the TPP function.
Only the units on the vertical axis change. Total factor Cost or Total Resource Cost is the product of the quantity of the input used in a production process times the price for that input. In a purely competitive market, individual buyers are assumed price takers.
This implies that the price of the input does not vary with the quantity an individual farmer purchases from the market. Profit is the difference between gross returns and total cost.
Profits are also referred to as net returns. The profit function for a farmer can be written as:. The optimal level of inputs is that level, which produces the highest level of profit. This level of input can be deduced using three criteria:. Thus the profit can be computed directly and the optimal level of input use is at the point where profit attains a maximum. Table 3 is given as an example of such a computation. Once Table 4. This can also be illustrated graphically as in Figure 4.
Based on data from Table 2 for example, profit can be expressed as a function of inputs. The optimum level of input occurs when profit is at maximum.
X 0 The production function expressed in Table 4. X — TFC. If the profit function is differentiated with respect to the variable input then, the optimal level of the input could be determined. Equation 4. This is the input criterion for profit maximization. It expresses both TVP and TC in terms of X Using this criterion, one can establish the optimal level of input and the corresponding level of output.
Profit is maximized when the two slopes are equal in the second stage of the classical production function. Thus, if the price of X and Y is known, the optimal level of the input and output can be computed. Solve for X in equation 4. Choice of Decision Criteria: Maximum Profit versus Maximum Yield When we determine the optimum level of variable inputs, we assume that the farmer had made the decision to pursue maximum profit as their goal.
However, sometimes farmers may want to pursue other goals such as maximum output for reasons that are best known to them. What is important to note here is that, unless inputs are free, the point where profit attains a maximum X1 is not the same as the point at which output is maximized X2. This is because the efficiency of using variable inputs declines in stage II of the production function. Beyond the point of maximum profit, the added inputs cost more than they earn, such that pursuing maximum output may lead to lower net returns or profit.
However, of inputs are free, both profit and output are maximized at the same point, X2. Iso-profit line Relative magnitude of profit before fixed cost. X X1 X2 Figure 4. TC Break even point. As is the case with the optimal level of input, optimal output can also be determined from a table e.
Table 4. Graphically, determination of optimal output is Y1 as illustrated in figures 4. Since farmers are assumed to sell in a purely competitive markets, then Py is constant why? Y — Pxf-I. Differentiating equation 4. This point occurs in stage II of the classical production function. However, a farmer may not have enough funds to purchase all the inputs required for profit maximization.
In such a special case, the farmer could operate in I, to the left optimal level of input, as long as net returns are positive. This is the portion of the MC in region II of the production function. That is, as long as they are able to cover variable costs. This portion of the MC curve is referred to as the derived supply curve for the individual producer.
It is important to note that in a purely competitive market, the individual producer farmer is unable to influence the market price for inputs or output. However, this cannot go on indefinitely. A firm that cannot meet its long run variable and fixed costs will eventually be driven out of business in the long run.
This excess profit or RENT accrues only in the short run. In the long run, other producers will be attracted by the RENT to enter the industry. This will increase. If there are any fixed costs, which cannot be varied during the production period, the firm is said to be operating in the short run.
The equilibrium is likewise referred to as the short run equilibrium. Derived Demand for Inputs Just as the marginal cost curve above the AVC is the short run supply curve for the individual producer, likewise, the value of the marginal product curve VMP can be interpreted as the derived demand curve for variable inputs for the individual producer. Thus as shown in Figure 4. PX4 PX3. AVP PX1. Opportunity Cost The opportunity cost of a resource is defined as the return that a resource can earn when it is put to its best alternative use.
For example a farmer with Kg of CAN fertilizer can apply it to one ha. Of maize or one ha of Irish potatoes. Suppose from maize the farmer will get an additional T. Shs 40,of maize while from potatoes the farmer will get T. Shs 45, worth of. Shs worth of additional maize. Thus the opportunity cost of the fertilizer is T. Shs 40, The opportunity cost of a shilling spent on consumption for example is the interest it could earn if deposited in the bank.
Concluding Comments Profit maximizing conditions for the firm have been derived. Profits are maximum when the level of output is chosen such that MC is equal to MR. The cost function is the inverse of the production function that underlies it.
Often however, the firm manager must simultaneously decide on the amount to be used for more than one variable inputs. In this section we will discuss criteria that are used for input mix decisions. We will maintain some of the assumptions introduced earlier where we has only one variable input. As such, input and product prices are taken as given. This implies that the farmer is operating in the short run where the law of diminishing returns applies. NOTE that if all inputs are varied, the law of diminishing returns does not hold.
When only one variable input is used, for a given technology, a given level of output can be produced only in one way remember, there is a one to one relationship between inputs and output in a production function.
When there are two or more variable inputs, a given level of output can be produced using different combinations of the variable inputs. This is because substitution occurs between some factors of production. Based on Table 5. Note that with the exception of the maximum and minimum level of production, all other output levels can be produced using several combinations of inputs. Conventionally, isoquants are represented graphically in two dimensions as in Figure 5.
However, if there are more than two imputs the isoquant would represent a surface. Isoquant Map. Mathematically, an isoquant can be derived by solving for one of the variable inputs X1 as a function of the other variable input X2 and Output Y.
An isoquant can be defined for every output level or conversely, every output has an isoquant. If they did they would violate a basic assumption of production functions, that is; each combination of inputs can produce only one level of output. However, many combinations of the variable inputs can result into a given level of output.
In fact, the entire loci of points along an isoquant represents different combinations of the variable inputs for a given level of the product.
A convex isoquant implies that production is within stage two of the classical production function, and the law of diminishing returns applies. If the isoquants were concave to the origin, decision makers would not be able to reach optimal decisions maxim or minimum , which means, conditions for economic efficiency would be violated. Some authors call it the marginal rate of technical substitution.
The MRS is a measurement of how one input substitutes for another as one moves along an isoquant to maintain the same level of production. In other words, the MRS is defined as the amount by which one input X1 must be reduced to maintain the same level of production when the other input X2 is increased by one unit.
Isoquants are convex to the origin, which means they are negatively sloped. Isoquants exhibit a diminishing marginal rate of substitution. The diminishing MRS for isoquants is directly related to the diminishing marginal product for each of the variable inputs. Each production function has its own. A convex isoquant implies production is taking place in stage II and therefore, diminishing marginal productivity.
X2 Figure 5. The average MRS is represented by the slope of the straight line connecting the arch between those two coordinates.
The exact MRS on the other hand is represented by the slope of the tangent to the isoquant at the specific point of interest. The exact MRS can only be obtained if a continuously differentiable isoquant is defined. The MRS is negative because isoquants are negatively sloped. For a convex isoquant, the absolute value of the slope changes continuously through the entire range of the isoquant, consistent with diminishing MRS as defined earlier. Exact MRS: This is defined by the line that is tangent to the isoquant.
If the isoquant given in equation 5. Apply this approach to our earlier production function given under Equation 5. It was state earlier that a production function is a technical relationship between inputs and output to guide production decisions. Isoquants are derived from production functions, and they serve the same purpose. Movement along an isoquant is done by the manager during the planning process to select the combination of inputs which will yield the highest level of profit.
That combination of inputs is referred to as the optimum combination of inputs. However, the exact shape of the isoquant map depends on the manner in which the inputs substitute for each other in the production process. In this respect, inputs may substitute for each other at a decreasing rate, at a constant rate, or in fixed proportions.
The isoquant map is therefore related to the nature of input substitution, which is in turn related to the underlying production function. Inputs as Technical Substitutes Inputs are said to be technical substitutes when an increase in one input permits a decrease in the other input while maintaining the same level of output. Such inputs are said to compete for each other and their MRS is negative,. Technical substitutes with Decreasing MRS If two inputs are technical substitutes, and the absolute value of the MRS decreases as one of the variable inputs increases while the other input decreases, then the rate of substitution is said to be decreasing See illustration in Figure 5.
Decreasing rates of substitution are caused by the law of diminishing returns. Examples of isoquants with decreasing MRS are shown in Figure 5. X2 X2 X2. If too much of one input is used, increasing amounts of the other input must be applied to maintain output at the same level. The zone of economic relevance is the portion, which has a negative slope. Beyond a certain unit, the absolute value of the MRS becomes very large since large quantities of the second input are required to replace small quantities of the first input in order to maintain the same level of output production.
This occurs when the rate at which inputs substitute for each other remain constant throughout the entire range of the isoquant. Constant rate of substitution requires that the slope of the given isoquant remains constant unchanged. This means the isoquant is a straight line with a constant slope, but, the isoquants do not have to be equidistance nor do they have to be parallel. Complementary inputs represent the opposite of substitutes. Some examples of complementary inputs in agriculture include: 1 parts which make a machine e.
In the case of complementary inputs, adding more of one of the inputs, beyond the required proportion will not reduce output, but it will not increase it either. The level of output will remain unchanged. Thus the input combination may be considered as one input eg tractor and tractor driver , which may substitute for other combinations. When isoquants degenerate into a dot, it means only one combination of inputs may be used to produce that given level of output.
Inputs that are not divisible are referred to as lumpy inputs eg a tractor. Such inputs appear only in discrete units. If both inputs are lumpy tractor and driver , then the isoquants would not be continuous.
Points would be connected by dotted lines as in Figure 5. Average and Exact Elasticity of Factor Substitution As is the case with average and exact MPP or MC, the average elasticity of substitution is derived when only two coordinates of an isoquant are defined. The continuous elasticity of factor substitution is defined when a continuously differentiable isoquant is defined, such that the MPP of both variable inputs can be computed and substituted into the elasticity of factor substitution equation as in Equation 5.
Nitrogen fertilizer and plant population in the production of maize or any other crop for that matter. Isocost Lines Each combination of inputs has a cost associated with it. The costs are variable because variable inputs are involved. In other words, isocost lines determine all combinations of inputs that cost the same amount. An isocoost line may be thought of as a budget constraint. That is the maximum amount of money available for the producer to purchase inputs. Note that isocost lines correspond to total cost TC functions, just as isoquants relate to production functions.
If the prices of variable inputs are known, the TVC can be computed for all input combinations. Based on this, one can derive the isocost line as follows;. The first term is the vertical intercept while the second is the slope of the isoquant Figure 5. TVC 0, PX2. O X2 Figure 5. As follows;. The two important aspects of an isocost line are it distance from the origin and its slope.
Changes in the TVC when input prices are constant shift the isocost line up or down accordingly. Changes in the input prices change the slope of the isocost line as more of the cheaper input will be substituted for the more expensive input. We said earlier that producers strive to maximize profit as their primary objective. However, sometimes cannot access all the variable inputs in quantities that are adequate to maximize profit, often because they face budgetary constraints.
Now if a producer has a given outlay of funds to purchase inputs, they would like to produce the output using those inputs at the least cost possible. That combination of inputs, which minimizes the cost of producing a given level of input is referred to as the least cost combination LCC of inputs. Graphically, for isoquants that are convex to the origin, the least cost combination occurs at the point where the isoquant is tangent to the isocost line.
Least Cost Combination X2,X1. Equation 5. Now if the level of production along a given isoquant is not at the LCC, it will mean that either,. Although we have said at the LCC the isocost line is tangent to the isoquant, this is only true for isoquants that are convex to the origin. These include;. By definition, the isoquant for lumpy goods is a set of points for certain input combinations, and these points are connected by dotted lines because the isoquant is not defined everywhere.
Nevertheless, the LCC may be geometrically determined as illustrated in figure 5. The LCC solution E for a lumpy good is often stable because it remains range for some range of the input prices ratio. Enter your email address to comment. Enter your website URL optional. Close this module Help Padhle build this community Contribute to Padhle to see more free content.
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MP is subject to the law of diminishing returns, being 6 37 6. The MPPL becomes the effective demand curve for labour, and equilibrium in the labour market The objective of this paper is to discuss the theoretical is where this curve meets the market wage line or supply underpinnings of the concept of production functions in curve.
After this point, any addition of labour will be costly Economics and show their applications in business. The and wasteful or loss making because MPPL will be lower or author therefore decided to use a qualitative approach as there less than the horizontal wage supply line. However, was no need to collect primary.
Also secondary sources were improvement in productivity of labour resulting from training, relied upon for this review paper. It is hoped that researchers education and labour reorganisation will shift MPP L upwards and students alike will find the discussion in this paper useful and then more labour will be demanded.
In a multi-factor environment, the entrepreneur will employ IV. Both The Law of Diminishing Returns operates everywhere in terms vary from firm to firm and within the manufacturing nature and was first written about by Adam Smith in in and service industries their usage differ Begg et al. This means that specialised machinery soon become obsolete and difficult to sell or dispose of as they are asset-specific or industry-specific. At that Development as well as for Innovation in such volatile point, it may strategize to have mergers, acquisitions, environments.
Economies of Scale and Returns to Scale-Determinants Economies of Scale and Scope Economies of scale are the returns to output as variable factor inputs are added. Here, there is distinction between organic or Economies of scope are those external economies of scale internal economies and external economies. Internal derived from various forms of integration in the supply chain. Factor combinations are determined by cost the firm operates at the optimum of AC curve or the Second and technological constraints.
Firms face both variable and Stage of production where AFC falls considerably as there is fixed costs. Relevant costs are costs arising from management adequate uptake or absorption of fixed factors or overheads decisions while Irrelevant costs are neutral of management Keat et al. All firms seek efficient size of plant size to operate Internal economies of scale, according to Grant both in the short and long run.
This is because they are profit comprises marketing economies, plant size technical maximizing.
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