A firm has a Cobb-Douglas production function that is homogeneous of degree one: q=ALk-a Derive the firm's long-run cost function as a function of output and factor prices. What is the cost function that corresponds to the estimated beer manufacturer's production function q=1.52L 0.4 K0.62 Let w be the cost of a unit of labor and r be the cost of a unit of capital. The expansion path, as a function of L, a, w, and r, is K=.