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## Types of Factor-Factor Relationships

- There can be three types of combinations of inputs:
- Some of the inputs can be combined only in fixed proportions. Hence, in such cases, there is no decision-problem.
- The substitution at constant rate occurs when each unit of input (X
_{1}) added every time would replace the same level of other input (X2). - The amount of one input (X1) required to substitute for one unit of another input (X
_{2}) for a given level of production increases or decreases as the amount of X_{2}used increases. Substitution at an increasing rate is not common in horticulture, but decreasing rate of substitution is more common. The slope of the iso-product curve in this case becomes less steep as more of X_{1}is used relative to X_{2}. - Substitution Ratio change as under:
- An iso-cost line is the line connecting all combinations of two inputs that could be purchased for a given budget.
- One possible way to determine the least-cost combination is to compute the cost of all possible combinations and then select the one with the minimum cost. This method is suitable where only a few combinations produce a given output and calculations involved are a few and simple. Suppose there are five combinations of inputs which can produce 85 units of output as given in table 6.5. The price per unit of X
_{1}is Rs.3 and of X2 Rs.4. The total outlay of each combination can be determined by simple multiplications. - Out of five combinations calculated in table 6.5 above, 3 units of X
_{2}and 6 units of X_{1}is the least cost combination of inputs i.e., Rs.30. through this method it is possible that the true least cost combination is not located because we do not consider many combination which may be there on the iso-quant to the right or to the leaf of the point. - Procedure for finding out least cost combination is a under,
- If at any point on the iso-quant Px
_{1}∆X_{1}is greater than Px_{2}∆X_{2}then the cost of producing the given output could be produced by increasing the use of X_{2 }and decreasing X_{1}, because the cost of added unit of X_{2}is less than the cost of the replaced units of X_{1}. - On the other hand if at any point on the iso-quant, Px
_{1}∆ X_{1}is less than Px_{2}∆ X_{2 }the cost of producing the specified quantity of output can be reduced by using less of X_{2}more of X_{1}. - Isoquants and iso-cost lines are drawn on the same graph for different levels of production and total outlay. The least cost combination is indicated by the point of tangency of the isoquants and iso-cost lines.
(i) Fixed proportion combinations of inputs i) Fixed Proportion Combinations (ii) Constant rate of substitution (iii) Varying rates of substitution ∆ X21 = ∆ X22 = ∆ X2n Substitution Ratio = ------------------------------∆ X11 = ∆ X12 = ∆ X1n iii) Varying Rate of Substitution Iso – cost Lines Simple Arithmetical Calculations Table 2 Least-cost Combination of Two Inputs for Producing an Output
∆X2 (i) Compute marginal substation ratio =[ ------------]^{1}
∆X1
Px1 (ii) Compute price ratio = [--------------] Px2 (iii) The least cost criterion is that MRS of X2 for X1 should be equal to Px2 / Px1 . Work out lest cost combination by equating ∆X2 Px2
--- =----
∆X1 Px1 Px1 (∆X1) = Px2 (∆X2) |

Last modified: Saturday, 23 June 2012, 10:29 AM