Reference no: EM131248244
Economics Assignment-
In this assignment, the goal is to study the evolution of per capita output in the Solow growth model with population growth and technological progress. Assume that total output is determined by Yt = Kαt(AtLt)1-α, where At is labor augmenting technical progress. Here, At+1 = (1+g)At, and g > 0. Suppose that the savings rate is equal to a fraction s and the capital depreciates at the rate δ, where 0 < δ ≤ 1. Hence, Kt+1 = (1- δ)Kt + sYt. Finally, assume that the population grows at the rate η > 0 each period.
A. Let kˆ be capital per effective unit of labor. That is, kˆt = Kt/AtLt. Derive a difference equation expressing kˆt+1 as a function of kˆ. Graph this difference equation. What are the steady states of this difference equation? Are they stable or unstable?
B. Derive an expression for the capital-output ratio, Kt/Yt, as a function of kˆt. If the parameters of the model stay constant, what can you say about the capital-output ratio in the long run? Does it grow? Derive the long run value of this ratio.
C. Derive an expression for per capita output, yt as a function of kˆt. Again, what is the value of yt in the long run? Derive an expression for this. What is the growth rate of yt according to this expression? Does this depend on the growth rate of population? On the growth rate of technical progress?
D. Let s = 0.2, α = 0.33 and let δ = .08. Suppose population grows at a rate of 1.5 percent per year and that per capita output grows at a rate of 1.5 percent per year along a steady state growth path. What value for g does this imply?
In simulations a - d below, each simulation starts with parameter values set as described above. Also assume that A0 = 1 and L0 = 1.
a. Suppose that capital per effective unit of labor is equal to its steady state value in period 0. In period 5, there is a permanent increase in the growth rate of technical progress from 1.5 percent per year to 3 percent per year. Simulate and graph the level and growth rate of per capita output for 50 periods (beginning with period 1). Use two separate graphs.
b. Assuming the economy starts at the same point as in part a, suppose that there is a great invention that doubles At in period 5. The growth rate after that, however, remains at 1.5 percent per year. Simulate and graph the level and growth rate of per capita output for 50 periods.
c. Now suppose there is a permanent increase in the growth rate of population from 1.5 percent to 3 percent per year in period 5 and no change in growth rate of technical progress. Again, simulate and graph per capita income and its growth rate for 50 periods.
d. Finally, assume that there is a massive wave of immigration that increases the level of the population by 20 percent in period 5 but that the growth rate after that remains at 1.5 percent per year. Again, simulate and graph per capita income and its growth rate for 50 periods.
e. Of these four cases, which led to a permanent change in the growth rate of living standards? Which led to the biggest permanent change in the level of living standards?
Discuss the influence industrial and organization psychology
: Explain why industrial/organizational psychology should be considered a science. Include an explanation of how descriptive and inferential statistics are used in I/O research. Discuss the influence industrial/organization psychology has had on org..
|
What is the aircraft flight path angle
: What are the velocity components of the aircraft when expressed in the aircraftfixed frame?
|
Why would a person believe this is the right option
: Why would a person believe this is the right option? What age do you think this person might be? What kinds of problems and successes is a person with this point of view likely to encounter during their lives?
|
Marketing a new line of televisions
: Select the communication channel that is best for marketing a new line of televisions in the United states (domestic market) and international market (Australia).
|
Derive an expression for the capital-output ratio
: Economics 164 Assignment. Derive an expression for the capital-output ratio, Kt/Yt, as a function of kˆt. If the parameters of the model stay constant, what can you say about the capital-output ratio in the long run? Does it grow? Derive the long ..
|
Divorce or perhaps discrimination based on race and religion
: Consider 1 human service issue. It might be the lack of affordable housing, poor schools, date rape, divorce, or perhaps discrimination based on race, religion, and disability. You are not limited to these. Consider possible causes for the social ..
|
What is the aircraft angle of attack
: What are the velocity components of the aircraft when expressed in the aircraftfixed frame?
|
What is the period of this circular motion
: After 150 seconds, what are the velocity components of the aircraft when expressed in the ground-fixed frame?
|
Compute the system''s transfer function
: Is the matrix A asymptotically stable, marginally stable, or unstable?
|