question 1 chapter 3, book Walsh (monetry theory and policy) Suppose the production function for shopping takes the form 1jl = c = ex (n,fmb,

where a and b are both positive but less than 1, and x is a productivity factor. The

agent's utility is given by v(c, l) = c1 - 1 (1 - ) + zl-ry 1 (1 - 17 ), where l = 1 - n ns,

and n is time spent in market employment.

a. Derive the transaction time function g(c, m) = ns.

b. Derive the money-in-the-utility function specification implied by the shopping production

function. How does the marginal utility of money depend on the parameters

a and b? How does it depend on x?

c. Is the marginal utility of consumption increasing or decreasing in m?