Consider a Solow-Swan economy with a Cobb-Douglas production function with a constant savings rate. Imagine that the population growth rate "n" is a decreasing function of capital and it has the following functional form: for low values of k it's constant at some high level. For intermediate levels of k, it decreases rapidly. And for high values of k the population growth rate is constant again. In other words, the population growth rate looks like : a. Why may the population growth rate look like this? (make sure you discuss its three components and how each of them may be a function of k in the real world) b. Does a steady state necessarily exist?
Consider a Solow-Swan economy with a Cobb-Douglas production function with a constant savings rate. Imagine that the population growth rate "n" is a decreasing function of capital and it has the following functional form: for low values of k it's constant at some high level. For intermediate levels of k, it decreases rapidly. And for high values of k the population growth rate is constant again. In other words, the population growth rate looks like : a. Why may the population growth rate look like this? (make sure you discuss its three components and how each of them may be a function of k in the real world) b. Does a steady state necessarily exist?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![**Consider a Solow-Swan economy with a Cobb-Douglas production function with a constant savings rate.** Imagine that the population growth rate "n" is a decreasing function of capital and it has the following functional form: for low values of \( k \) it's constant at some high level. For intermediate levels of \( k \), it decreases rapidly. And for high values of \( k \) the population growth rate is constant again. In other words, the population growth rate looks like:
[Graph Description: The graph is shaped like a step function. It starts at a high constant level, drops sharply for intermediate levels of \( k \), and then becomes constant again at a lower level for high values of \( k \).]
**Questions:**
a. Why may the population growth rate look like this? (make sure you discuss its three components and how each of them may be a function of \( k \) in the real world)
b. Does a steady state necessarily exist?
c. Will the steady state be necessarily unique?
d. Will the steady state(s) be stable?
e. Will there be a "poverty trap"? (define poverty trap)
f. How can this model be used (and how has this model been used) to justify large increases in foreign development aid?
g. Discuss THREE potential flaws of the "population poverty trap" model.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10fa051a-d9bc-4043-b538-02be11dabc4b%2F3217a16e-197c-427d-acd1-d24dd83266c8%2Fx9je6vr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Consider a Solow-Swan economy with a Cobb-Douglas production function with a constant savings rate.** Imagine that the population growth rate "n" is a decreasing function of capital and it has the following functional form: for low values of \( k \) it's constant at some high level. For intermediate levels of \( k \), it decreases rapidly. And for high values of \( k \) the population growth rate is constant again. In other words, the population growth rate looks like:
[Graph Description: The graph is shaped like a step function. It starts at a high constant level, drops sharply for intermediate levels of \( k \), and then becomes constant again at a lower level for high values of \( k \).]
**Questions:**
a. Why may the population growth rate look like this? (make sure you discuss its three components and how each of them may be a function of \( k \) in the real world)
b. Does a steady state necessarily exist?
c. Will the steady state be necessarily unique?
d. Will the steady state(s) be stable?
e. Will there be a "poverty trap"? (define poverty trap)
f. How can this model be used (and how has this model been used) to justify large increases in foreign development aid?
g. Discuss THREE potential flaws of the "population poverty trap" model.
Expert Solution
Step 1
In a Solow-Swan economy with a Cobb-Douglas production function, savings rate is an increasing function of capital and it will have effect: for low values of k the savings rate is constant at some low level. For intermediate levels of k, the savings rate increases rapidly. For high values of k, the savings rate is constant again.
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