The text discussed the expansion path as a graph that shows the cost-minimizing input quantities as output changes, holding fixed the prices of inputs. What the text didn't say is that there is a different expansion path for each pair of input prices the firm might face. In other words, how the inputs vary with output depends, in part, on the input prices. Consider, now, the expansion paths associated with two distinct pairs of input prices, (w1, r1) and (w2, r2). Assume that at both pairs of input prices, we have an interior solution to the cost-minimization problem for any positive level of output. Also assume that the firm's isoquants have no kinks in them and that they exhibit diminishing marginal rate of technical substitution. Could these expansion paths ever cross each other at a point other than the origin (L = 0, K = 0)?