![]() A function is said to be homogeneous of degree n if the multiplication of all of the independent variables by the same constant, say λ, results in the multiplication of the independent variable by λ n. Typically economists and researchers work with homogeneous production function. At first the two economists have applied their principle to. Production functions may take many specific forms. This is similar to linear homogeneous production function showing constant returns to scale. Thus, the expansion path is a straight line. this function exhibits constant returns to scale and 1. The variable 'I' is hypothesized to influence significantly the partial production elasticities and, hence, the scale returns. 1Although Cobb-Douglas does restrict the elasticity of substitution between the demand for. Express the B's in (1) as follows: B1 Bj(I) (2) B2 B2(I) B3 B3(I). Increasing returns to scale with diminishing marginal product/utility (Quasiconcave y/U). Cobb-Douglas linear homogenous production function is a good example of this kind. Since output has increased by 50%, the inputs will also increase by 50% from 10 units of labour to 15 and from 5 units of capital to 7.5. Modified Cobb-Douglas Functions with Variable Production Elasticities Assume the Cobb-Douglas function (1): (1) Y A XlB1X2B23B3. Anatomy of a Cobb-Douglas Type Production/Utility Function. This is known as homogeneous production function. In addition, the assumption of constant returns to scale (or homogeneity of degree one in input quantities) implies that. Consequently, the cost minimising capital-labour ratio will remain constant. ![]() Since input prices do not change, the slope of the new isoquant must be equal to the slope of the original one.īut, the slope of the isoquant is the MRTS, which is constant along a ray from the origin for linearly homogeneous production function. Now, suppose, the firm wants to expand its output to 15 units. and capital, constant returns to scale, no unobserved inputs and perfect competition. To verify this point, let us start from an initial point of cost minimisation in Fig.12, with an output of 10 units and an employment (usage) of 10 units of labour and 5 units of capital. The Cobb-Douglas production function is often used to analyse the. If a firm employs a linearly homogeneous production function, its expansion path will be a straight line.
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