Explain the functional forms of cost function giving illustration
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1. Linear Cost Function:
A linear cost function may be expressed as follows:
TC = k + ƒ (Q)
2. Quadratic Cost Function:
If there is diminishing return to the variable factor the cost function becomes quadratic. There is a point beyond which TPP is not proportionate. Therefore, the marginal physical product of the variable factor will diminish.
And if TPP actually falls MPP will be negative. In other words, there is a point beyond which additional increases in output cannot be made. So costs rise beyond this point, but output cannot.
3. Cubic Cost Function:
In traditional economics, we must make use of the cubic cost function as illustrated in Fig. 15.5. Such a cost function is not of much empirical use. It does not provide statistically significant improvements over the linear or quadratic cost function. Moreover, it is very difficult to calculate, interpret and apply, to test statistical hypothesis regarding cost behaviour in manufacturing concerns.
The cubic cost function is based on three implicit assumptions:
1. When Q = 0, total cost is equal to total fixed cost.
2. Total fixed cost remains constant at levels of output up to capacity (as in the previous two cases).
3. With an output expansion there is an initial stage of increasing return to the variable factor; thereafter a point is reached (the inflection point) at which there is constant return to the variable factor; finally, there is diminishing return to the variable factor. In short, the cubic cost curve has two bends, one bend less than the highest exponent of Q.
A linear cost function may be expressed as follows:
TC = k + ƒ (Q)
2. Quadratic Cost Function:
If there is diminishing return to the variable factor the cost function becomes quadratic. There is a point beyond which TPP is not proportionate. Therefore, the marginal physical product of the variable factor will diminish.
And if TPP actually falls MPP will be negative. In other words, there is a point beyond which additional increases in output cannot be made. So costs rise beyond this point, but output cannot.
3. Cubic Cost Function:
In traditional economics, we must make use of the cubic cost function as illustrated in Fig. 15.5. Such a cost function is not of much empirical use. It does not provide statistically significant improvements over the linear or quadratic cost function. Moreover, it is very difficult to calculate, interpret and apply, to test statistical hypothesis regarding cost behaviour in manufacturing concerns.
The cubic cost function is based on three implicit assumptions:
1. When Q = 0, total cost is equal to total fixed cost.
2. Total fixed cost remains constant at levels of output up to capacity (as in the previous two cases).
3. With an output expansion there is an initial stage of increasing return to the variable factor; thereafter a point is reached (the inflection point) at which there is constant return to the variable factor; finally, there is diminishing return to the variable factor. In short, the cubic cost curve has two bends, one bend less than the highest exponent of Q.
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