Homework Help is Here – Start Your Trial Now!
Business
Economics
5. Find the supply function and the input demand functions for the CES production function: f(#1, F2) = A(ax{ +(1 – a)a%)8/e, where A > 0, B > 0, 0 < a < 1, and 0 + p< 1. Lind tho funoticon for t he CEs ndu funotion

5. Find the supply function and the input demand functions for the CES production function: f(#1, F2) = A(ax{ +(1 – a)a%)8/e, where A > 0, B > 0, 0 < a < 1, and 0 + p< 1. Lind tho funoticon for t he CEs ndu funotion

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
See similar textbooks
icon
Related questions
Question

Q5 solution needed 

1. Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1, x2) = (x1 – 1)0.25 9-5. Assume the price of input 1 is r and the price of input 2 is w.. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm? 2. Show that the profit function is convex in (p, w). 3. Find the profit function for the Cobb-Douglas production function f(x1, 12) = Axa with A > 0, a1, a2 > 0 and a1 + a2 1. 4. Verify Hotelling's Lemma for the Cobb-Douglas production function with a1+a2 < 1. 5. Find the supply function and the input demand functions for the CES production function: f(T1, #2) = A(ax{ +(1 – a)a%)8/e, %3D where A > 0, B > 0, 0 < a < 1, and 0 + p< 1. 6. Find the profit function for the CES production function. 7. Verify Hotelling's Lemma for the CES production function with B < 1.
Transcribed Image Text:1. Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1, x2) = (x1 – 1)0.25 9-5. Assume the price of input 1 is r and the price of input 2 is w.. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm? 2. Show that the profit function is convex in (p, w). 3. Find the profit function for the Cobb-Douglas production function f(x1, 12) = Axa with A > 0, a1, a2 > 0 and a1 + a2 1. 4. Verify Hotelling's Lemma for the Cobb-Douglas production function with a1+a2 < 1. 5. Find the supply function and the input demand functions for the CES production function: f(T1, #2) = A(ax{ +(1 – a)a%)8/e, %3D where A > 0, B > 0, 0 < a < 1, and 0 + p< 1. 6. Find the profit function for the CES production function. 7. Verify Hotelling's Lemma for the CES production function with B < 1.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS