# Why may the population growth rate look like this?

Problem 4 Consider a Solow-Swan economy with a Cobb-Douglas production function with Show more Problem 4 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 its 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 : 1. 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) 2. Does a steady state necessarily exist? 3. Will the steady state be necessarily unique? 4. Will the steady state(s) be stable? 5. Will there be a poverty trap? (define poverty trap) 6. How can this model be used (and how has this model been used) to justify large increases in foreign development aid? 7. Discuss THREE potential flaws of the population poverty trap model. Problem 5 Consider a Solow-Swan economy with a Cobb-Douglas production function. Imagine that the savings rate s is an increasing function of capital and it has the following functional form: 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. In other words the savings rate looks like 1. Does a steady state necessarily exist? 2. Will the steady state be necessarily unique? 3. Will the steady state(s) be stable? 4. Will there be a poverty trap? (define poverty trap) 5. How can this model be used (and how has this model been used) to justify large increases in foreign development aid? 6. Discuss THREE potential flaws of the savings poverty trap model. Problem 6 Consider a Solow-Swan economy with a Cobb-Douglas production function Y = AK ? L 1?? with A = 10 and ? = 1/2. The depreciation rate is ? = 0.09 and the rate of population growth is n = 0.01 1. Write down the fundamental equation of Solow-Swan in terms of the savings rate s Imagine that the savings rate is s = 0.20 for economies with capital per person k < 1000 and s = 0.70 for economies with k > 1000 2. Plot the basic functions of the Solow-Swan model. That is plot the savings function and the depreciation line as functions of capital 3. What is the steady state capital stock k ? for economies with k < 1000? 4. What is the steady state capital stock k ? for economies with k > 1000? 5. Consider an economy in the k < 1000 steady state. Imagine that it receives a donation of capital of D = 300 dollars per person. What happens to this economy over time? 6. Consider an economy in the k < 1000 steady state. Imagine that it receives a donation of capital of D = 700 dollars per person. What happens to this economy over time? 7. Do small donations help countries escape out of their traps? Explain intuitively. Show less