Consider the production function for a single output, single input firm: f(L) = ln (1+L). Assume that L 0, wage rate is w, and the output price is 100.There is no fixed factor.This problem should get you comfortable with the names for the different functions.

a. What is the profit maximization problem corresponding to this production function?(Remember: profit = total revenues - total costs.)Be as specific as the problem allows.

b. What is the set of first order condition(s) for the profit maximization function (your control variable is L)?

c. Write the factor demand function for this output. (That is, L = ?Use your answer from (b).)

d. Write the supply function for this output. (That is, q = f(L) but expressed not in terms of L, but in terms of factor price w.)