Enclosed I send you the homework. I would expect detailed solutions. Please let me know if you are able to do it and what is the price
Micro II: Homework problem II Bartlomiej Wisnicki Deadline: 07.05.2019 Each of these exercises is graded separately. Write the solutions with explanations. Unexplained answers will not be graded. You can bring the solutions to the classes or send them to
[email protected]. If you do the latter, name the message: ”Microeconomics II, homework problem II”. The attached file ought to be a one pdf file with signed papers. 1. Suppose that a firm has access to two production technologies for the production of some good x: c1(x1) = 1 2 ω1x 2 1, c2(x2) = ω2x2, where ω1, ω2 > 0 are production cost parameters. (a) Given a required output X = x1 + x2, and the fact that x1, x2 ≥ 0, find amount of x1(ω1, ω2, X) and x2(ω1, ω2, X) that will minimize the production cost for any given input prices and output requirements. Write the form of the function c(ω1, ω2, X) as minimum cost conditional of production X units of a good. (b) Suppose ω1 = ω2 = 1. The firm uses the good produced in part a) to produce a good y according to the following function: y = px1/2. Calculate profit maximizing output y(p) and optimal profit π(p). 2. Suppose the production function is given by F (K,L) = (min(2K,K + L))α, where α > 0. Assume the price of output is p, the input prices are: r, k. Naturally, we want to maximize the profit for given prices. Find the (a) input demand functions x1(p, r, w, α), x2(p, r, w, α) (the function of optimal com- binations of inputs for given prices and parameter α); (b) supply function y(p, r, w, α) (the function of optimal output production for given prices and parameter α); (c) profit function π(p, r, w, α) (the function of optimal profit for given prices and parameter α). 1