280
UNIT 2 INPUT- INPUT RELATIONSHIPS
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3.0 MAIN CONTENT 3.1 Substitution Ratio
You will recall in the previous unit, the relationship we considered was that between a variable input and the output while other inputs are held constant. In this unit we shall consider the case where there are two variable inputs instead of one. There is bound to be relationship between the two variable inputs on one hand and of course relationship between the two variable inputs and the output itself. The isoquant is a curve that connects the various combinations of the two variable inputs that can be used to produce the same level of output.
As mentioned earlier the problem facing the financial manager here is to determine which of these numerous combinations of the variable inputs will give the least cost in producing the specified level of output represented by that particular isoquant. This question cannot be answered until we know how much each of the variable inputs costs. We therefore bring prices of the variable inputs into the picture.
There is a line called isocost line. The isocost line connects the various combinations of the variable inputs that can be purchased at the same cost. “Iso” means equal. “Isocost” means equal cost. Therefore, for the purpose of determining the least cost combination of inputs for producing a given level of output the first step lies in finding out the substitution ratio of the two inputs in question. Substitution ratio is determined from the following expression.
Substitution ratio=
1 2
X X added
input of Quantity
replaced input
of Quantity
This substitution ratio is also called Marginal Rate of Technical Substitution (MRTS).
If there is a constant rate of substitution between the inputs, corresponding isoquants will be a straight line (Figure 5).
282 X
X X X 2 X
X
y
X2 X
0 X1
Fig. 1.5: Linear isoquant Fig. 1.6: Convex isoquant
In the case of diminishing rate of substitution the isoquant is convex to the origin as shown in Figure 6. Isoquants and indifference curves exhibit similarity to a large extent. Various combinations of two inputs for producing a given amount of output depict an isoquant, while indifference curve shows various combinations of two consumable goods that yield a given amount of satisfaction. Keeping in view this similarity, isoquants are frequently addressed as production indifference curves. The slope of the isoquant is negative and its absolute value indicates the marginal rate of technical substitution (MRTS). Isoquants are convex to the origin.
In the case of Leontief isoquant the substitution ratio is fixed and the isoquant takes the shape of a right angle triangle as shown in Figure 7.
Fig. 1.7: Leontief Isoquant
In order to find out the optimal level of input combination the ratio of input prices is compared with the substitution ratio. Price ratio is defined as follows:
Price ratio =
2 1
Pr Pr
PX PX replaced
being input of ice
added being
input of
ice .
This price ratio is also the slope of the isocost line.
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The least cost combination of inputs will be at a point where the substitution ratio (MTRS) and inverse price ratio are equal. The least cost principle is shown with the help of livestock data in Table 3 and its diagrammatic representation in Fig. 8. This principle helps the financial manager in allocating the limited finance in purchasing two important substitutable inputs.
Y
X2
O X
1 X
Isoquant
Least Cost Point
ISOCost line
Fig. 1.8: Least Cost Combination of Two Inputs
Costs are at minimum point, where, input substitution ratio (MTRS) is equal to inverse of the price ratio. This is the point of tangency between the isocost line and the isoquant. From the Table, it is found at the feed combination “F”. Substitution ratio will remain the same over time, provided physical/biological relationships do not change. The price ratio changes if relative input prices change. In the hypothetical example, it is assumed that prices will not change. As the price of one input increases compared to another, the existing least cost combination tends to change.
3.2 Decision Rule
If the Substitution Ratio is greater than Price Ratio, the total cost of feed ration can be reduced by moving downwards to the succeeding ration in the Table. If the Substitution Ratio is less than Price Ratio, the converse holds good.
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Table 3: Selecting Least Cost Feed Ration for Producing 25 kg Body weight
Feed
combination
Grain (kg) Hay (kg) MRTS Price
Ratio (X1) X1 (X2) X2 X1 for
X2
Px2/Px1 A
B C D E F G H I J K
500 550 600 650 700 750 800 850 900 950 1000
50 50 50 50 50 50 50 50 50 50
2190 2065 1943 1825 1715 1610 1512 1425 1349 1289 1233
125 122 118 110 105 98 87 76 60 56
2.5 2.44 2.36 2.20 2.10 1.96 1.74 1.52 1.20 1.12
2.10 2.10 2.10 2.10 2.10*
2.10 2.10 2.10 2.10 2.10 *Optimum combination
SELF-ASSESSMENT EXERCISE
What is the relationship between marginal rate of technical substitution and least cost combination of inputs.
4.0 CONCLUSION
You learnt about the relationship between two variable inputs for producing a certain level of output. The relationship is in the way they substitute for each other.
5.0 SUMMARY
In this unit you have learnt that:
An isoquants connects various combinations of inputs that can be used to produce the same level of output.
An isocost connects the various combinations of two variable inputs that can be purchased at the same cost.
When the isocost line is tangent to the isoquant, the point of least cost combination of the variable inputs is determined.
This point of tangency corresponds to where the Marginal Rate of Technical substitution is equal to the ratio of prices of the two variable inputs i.e.
285 1
2
X X added
input of Quantity
replaced input
of Quantity
=
2 1
Pr Pr
PX PX replaced
being input of ice
added being
input of
ice
6.0 TUTOR-MARKED ASSIGNMENT
1. Define the following terms:a. Isoquant b. Isocost line
c. Marginal Rate of Technical Substitution d. Least Cost Combination of inputs.
2. Given that Px1= 100 Px2 = 200, determine the least cost combination of inputs X1 and X2 by completing the table below.
Units of X1
Units of X2
Cost of X1 Cost of X2 Total outlay 4
6 8 10 12 14 16 18 20
24.2 18.2 16.2 15.0 14.4 14.2 14.4 14.0 14.4
7.0 REFERENCES/FURTHER READING
Olukosi, J. O. & Ogungbile, A. O. (2008). Introduction to Agricultural Production Economics: Principles and Applications, Nigeria:
AGITAB Publishers Ltd.
Olukosi, J. O. & Alamu, J. F. (2013). Introduction to Agricultural Finance: Principles and Applications. Nigeria: Great Glory Publishers.
Olukosi J. O. & Erhabor P. O. (2012). Introduction to Farm Management Economics: Principles and Applications. Nigeria:
AGITAB Publishers Ltd.