a) state the maximization problem solved by each type of agent and derive the fist order and second order conditions. Derive the solution using the implicit function theorem. b) Determine the equilibrium conditions for the three markets using the resource constraints and the budget constraints. provide statement of the equilibrium c) Assume logarithmic utility U(c)=In(c) and derive a closed form solution for consumption in both periods and savings for both types of agents d) Solve the social planning problem. Compare the solution of the social planning problem with the competitive equilibrium. Demonstrate that the decentralized solution solves the social planning problem for a particular set of pareto weights. Explain how this is an example of the first welfare theorem.

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

Constructing an equilibrium

Households live two periods and have prefernces

U(c1)+βU(c2)

where 0<β<1 and U is the utility function and satisfies our usual assumptions. There are N households in the economy. N1 of these have endowments y1 in the first period and no endowment in the second-these agents are called "Type 1". The remaining N2 have no endowment in the firs period and y2 in the second period- these agents are called "Type 2". Hencethe resources of the economy are 

N1y1

in the first period and 

N2y2 in the second, where

N=N1+N2

Households have access to a credit market where the can borrow  (s<0) or save s<0. The type 1 agent faces budget constraints

y1=c11+s1

rs1=c21

where the consumption for the type i agent in period j is denoted cji. The type 2 agent faces budget constraints

0=c12+s2

y2+rs2=c22

The resource constraints are

N1y1=N1c11+N2c12

N2y2=N11c21+N2c22

a) state the maximization problem solved by each type of agent and derive the fist order and second order conditions. Derive the solution using the implicit function theorem.

b) Determine the equilibrium conditions for the three markets using the resource constraints and the budget constraints. provide statement of the equilibrium

c) Assume logarithmic utility U(c)=In(c) and derive a closed form solution for consumption in both periods and savings for both types of agents

d) Solve the social planning problem. Compare the solution of the social planning problem with the competitive equilibrium. Demonstrate that the decentralized solution solves the social planning problem for a particular set of pareto weights. Explain how this is an example of the first welfare theorem.

Expert Solution
steps

Step by step

Solved in 5 steps with 25 images

Blurred answer
Knowledge Booster
Cobb-Douglas Production Function
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
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