Ford Motors uses labor (workers) and capital (robots) to make cars. Specifically, if they
hire l units of labor and use k units of capital, they can make:
f (l, k) = √l + 4√k
cars. Suppose the price of cars is p, the price of labor is w and the price of capital is 1.
(a) Write Ford’s profit, Π, in terms of p, w, l and k.
(b) Find ∂Î
∂l and ∂Î
∂k , in terms of p and w.
(c) To maximize Î , set ∂Î
∂l = 0 and ∂Î
∂k = 0. This gives you two equations and two
unknowns (l and k, since from Ford’s perspective, p and w are known). Solve for the
profit-maximizing l and k, in terms of p and w.
(d) To check your answer, make up values for p and w (for example, p = 10 and w = 2).
Using these p and w, find the numerical value of Ford’s optimal l and k and maximum Π.
Then, make up two other pairs of l and k, and check that they give lower profi