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5 Cost Models > Homotheticity - Pg. 150

150 CHAPTER | 5 Cost Models HOMOTHETICITY It is also informative to look at relationships between output and the input prices, as the input price­output interaction terms allow for the nonhomotheti- city of the underlying production function. As described in their 1976 paper, Christensen and Greene write: "A cost function corresponds to a homothetic production function if and only if it can be written as a separable function in output and factor prices." 4 Homothetic functions are functions of which the marginal technical rate of substitution (slope of the isoquant) is homogeneous of degree zero. Due to this, along rays coming from the origin, the slope of the isoquants will be the same. What this implies for the translogarithmic cost function is that iy = 0 (5.28) for all i = 1, ... , n. Coefficients of the input price­output interaction terms measure how a change in an input's price affects its usage and how the change in its usage affects output, which then affects the total cost of distributing electricity. For example, an increase in the wage rate will most likely cause less labor to be employed, thus causing a reduction in output, which, in turn, will affect the