Wanda runs a rm that produces some of the coziest scarves you will ever see. Anyone can see

how cozy they are. What you might not expect is that some of them are produced by hand, while

others are produced by a eet of robots. In fact, Wanda would say that her production function is

f(K,L) = 2 K + L. It only costs Wanda a wage rate of w = 10 per human worker, but a rental rate of r = 40 for each one of her knitting robots.

(a) Assuming that Wanda is cost-minimizing, in the long-run, what fraction of her scarves will be made by humans? (Note: since K and L do not interact in our production function, we are

interpreting 2 K as the number of scarves made by robots, and L as the number made by humans.)

(b) Solve for Wanda's long-run total cost function. What is her long-run marginal cost function?

(c) After an unfortunate incident and some very bad PR, Wanda has to hire a newpublic relations rm to convice the local population it is safe for her to have those robots. Accordingly, Wanda has a xed cost of $1000 that she has to pay to the PR rm, regardless of how many scarves she actually produces. Solve for Wanda's long-run average total cost function.