2. Consider profit maximization problem described in the slides of the Chapter 19
$\min_{x_1, x_2} \pi(x_1, x_1) = py - w_1x_1 - w_2x_2$
y = f(x_1, x_2)$
where f(x_1, x_2) = x_1^{1/3}x_2^{1/3}$.
a) The above profit maximization problem is solved by using short-run and long
run maximization. Study this solution and make sure that you can reproduce it on the
exam.
b) Derive the same solution by direct maximization of the profit function assuming
that both inputs can be adjusted.
c) Show graphical solution using the tangency of the production and profit function.
d) Explan why long run maximization of short run profits leads to the same solution
as maximization with respect to both inputs simultaneously.
