1.1) The production function of the firm is F(l) = 4l + 2l^2 l^3 l [0, 2].

(1) a. Compute for the proper domain. Indicate the image for each one

(a) AP(l)

(b) MP(l)

b. Determine the value of l that maximizes AP(l)

c. Illustrate the MP and AP functions on the same graph

d. State precisely the problem the firm must solve to determine its demand for labor when it faces an output price p and wage w

e. Given p > 0, at what wage rate, if any will the firm demand:

(a) 1/3 units of labor

(b) 1 unit of labor

(c) 4/3 units of labor

1.2) What happens to a competitive firm whose cost functions exhibit decreasing marginal cost everywhere? Construct a concrete cost function of this type & carry out the search for the profit-maximizing function.

1.3) Avianca flies regularly between Yopal and Karkadu. It can discriminate between business and pleasure travelers and deal with separate markets by imposing conditions such as staying one Saturday night and advance purchases. Let Q = 16 p denote the demand for business travelers and Q = 10 p the demand for pleasure travelers. Suppose the cost function for all travelers is given by C(Q) = 10 + Q2. How much should Avianca charge in each market to maximize its profits? How would you use Matlab to solve the resulting system of equations?