Question 3. Consider a market where demand is given by the function q8 = a – bp., a, b > 0, t = 0,1,2, ... and supply is given by the function qi = m + nE̟-1(P;), n > 0 Where E-1 is the expectation of price in period t – 1, which is given by E-1 (Pt) = ôpt-1 + (1 – 8)ỹ, 0 < 8 <1 a) Assume that the price adjusts to clear the market. Find p, as a function of pe-1- What kind of difference equation have you derived? b) Find the steady-state value of price. Explain your working. c) Find the solution to the difference equation as a function of the initial price po, time t, and the parameters of the model (a, b, m, n). d) For a steady-state price p, say p, rewrite the solution you find in part (a). What determines whether på converges to, or diverges from, the steady-state price p?
Question 3. Consider a market where demand is given by the function q8 = a – bp., a, b > 0, t = 0,1,2, ... and supply is given by the function qi = m + nE̟-1(P;), n > 0 Where E-1 is the expectation of price in period t – 1, which is given by E-1 (Pt) = ôpt-1 + (1 – 8)ỹ, 0 < 8 <1 a) Assume that the price adjusts to clear the market. Find p, as a function of pe-1- What kind of difference equation have you derived? b) Find the steady-state value of price. Explain your working. c) Find the solution to the difference equation as a function of the initial price po, time t, and the parameters of the model (a, b, m, n). d) For a steady-state price p, say p, rewrite the solution you find in part (a). What determines whether på converges to, or diverges from, the steady-state price p?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
100%
I need the full answers of all parts correct and fast please
Transcribed Image Text:Question 3. Consider a market where demand is given by the function
qº = a –
bpt, a, b > 0, t = 0,1, 2, ...
and supply is given by the function
qi = m + nE̟-1 (Pt),
n > 0
Where E-1 is the expectation of price in period t – 1, which is given by
E-1 (Pt) = 8p;-1 + (1 – 8)P,
0 < 8 < 1
a) Assume that the price adjusts to clear the market. Find p, as a function of p¿-1-
What kind of difference equation have you derived?
b) Find the steady-state value of price. Explain your working.
c) Find the solution to the difference equation as a function of the initial price po,
time t, and the parameters of the model (a, b, m, n).
d) For a steady-state price p, say p, rewrite the solution you find in part (a). What
determines whether p, converges to, or diverges from, the steady-state price p?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
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