The production functions display the standard properties, including constant returns to scale. A representative household has utility U(ca, Cs) where c; is the consumption of good i. The total supply of each factor is fixed K = Ka+K, L = La+L
The production functions display the standard properties, including constant returns to scale. A representative household has utility U(ca, Cs) where c; is the consumption of good i. The total supply of each factor is fixed K = Ka+K, L = La+L
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question

Transcribed Image Text:3. First and Second Welfare Theorems
There are two goods A and B and two inputs K and L. The production functions are
AKLI-a
BKL
Ya
%3D
Y, =
The production functions display the standard properties, including constant returns
to scale.
A representative houschold has utility
U(Ca, Cs)
where c; is the consumption of good i. The total supply of each factor is fixed
K
Ka + K,
L = La+ Lo
duetion

Transcribed Image Text:Now assume a market system.
i. Households own the labor and capital, which is rented to firms. The household
faces a budget constraint
wa La + wLb +raKa+ r¿K½ > PaCa + PbCb
where wi is the real wage paid in industry i and r; is the rental rate in
industry i. The total supply of each factor is fixed, as described above. Solve
the household's maximization problem.
ii. Firms maximize profits. A firm's profits in industry A are
Ta = PaFa(Ka, La) – waLa – raKa
and a firm's profits in industry B are
Ty = PoF,(Kb, Lt) – wrL – r&K,
Solve the maximization problem for each firm.
iii. State the equilibrium conditions assuming households and firms are price-
takers.
Expert Solution

Step 1
Given information
Household utility function: U(ca ,cb)
There are 2 goods and 2 inputs given
Production function:
For good A
Ya = A Kaα La 1-α
For good B
Yb = B Kbβ Lb1−β
Step by step
Solved in 3 steps with 2 images

Recommended textbooks for you


Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON

Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON


Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON

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)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning

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-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education