QUESTION Assume that the output of a certain type products produced by a firm using K units of capital and L units of labor is
QUESTION
Assume that the output of a certain type products produced by a firm using K units of
capital and L units of labor is given by the Cobb-Douglas production function: 1
Q=f(K,L)=K L .
We also assume that the firm's budget constraint is given by
R K + W L = S,
where R, W and S denote respectively, the interest rate, wage rate, and available fund in dollars. The firm aims to find out the amount of capital and labor input, at which the firm can achieve the maximum output subject to the budget constraint.
(1) DerivetheLagrangianfunction,whichisthefunctiontobemaximisedsubjecttothe budget constraint.
(2) Find the values of K and L, at which the firm can use to maximise its output, assuming = 0.5, R = 0.1 (or 10%), W = $10 (per unit of labor) and S = $100.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get step-by-step solutions from verified subject matter experts
100% Satisfaction Guaranteed-or Get a Refund!
Step: 2Unlock detailed examples and clear explanations to master concepts
Step: 3Unlock to practice, ask and learn with real-world examples
See step-by-step solutions with expert insights and AI powered tools for academic success
-
Access 30 Million+ textbook solutions.
-
Ask unlimited questions from AI Tutors.
-
Order free textbooks.
-
100% Satisfaction Guaranteed-or Get a Refund!
Claim Your Hoodie Now!
Authors: Mark Daniel Ward, Ellen Gundlach
1st edition
716771098, 978-1319060893, 1319060897, 978-0716771098
Study Smart with AI Flashcards
Access a vast library of flashcards, create your own, and experience a game-changing transformation in how you learn and retain knowledge
Explore Flashcards
