4. (Walsh 2010 p 130) Suppose the production function for shopping is e"(ns)amb, where c a E (0,1) and b e (0, 1), and a is a productivity factor. The agent's utility function is v(c,l) cl-b/(1-) +11-n/(1-), where l = 1-n-n8 (a) Derive the transaction time function n g(c, m). (b) Derive the MIU functional form implied by this shopping production function p. (c) How does the marginal utility of money depend on a, b, and z? Is the marginal utility of con- sumption increasing or decreasing in m? 4. (Walsh 2010 p 130) Suppose the production function for shopping is e"(ns)amb, where c a E (0,1) and b e (0, 1), and a is a productivity factor. The agent's utility function is v(c,l) cl-b/(1-) +11-n/(1-), where l = 1-n-n8 (a) Derive the transaction time function n g(c, m). (b) Derive the MIU functional form implied by this shopping production function p. (c) How does the marginal utility of money depend on a, b, and z? Is the marginal utility of con- sumption increasing or decreasing in m