Cost-Share Equations 145 In this case, they employed a single-output, three-input translog cost function, which is given by ln C = 0 + y ln y + i i ln p i + ð1=2Þ yy ðln yÞ 2 + ð½Þ i j ij ln p i ln p j + i iy ln y ln p i , (5.12) where output (ln y) and input prices (ln p i ) enter linearly, as quadratics and as cross-products. This is one of the specifications estimated later in this chapter, as well as being used in the examples and exercises at the end of the chapter. COST-SHARE EQUATIONS Cost-share equations allow for the assumption of cost-minimizing behavior to be imposed on the model. In general, the equation for the ith input price is given by (via Shephard's lemma, which was defined in Chapter 4): (5.13) s i = ln C ln p i , that is, s i = i + ii ln p i + i lnY + ð1 2Þ j ij ln p j (5.14)