Question

In: Economics

Consider the standard Solow growth model. Let productivity be denoted by A and let the production...

Consider the standard Solow growth model. Let productivity be denoted by A and let the production function be Y=AF(K,N). For Simplicity, assume that there is no population growth (n=0 so that N' = N). let depreciation be denoted by d and the savings rate by s.

a) Derive the per capita capital accumulation equation for k=K/N and the steady state level of capital per worker, ??^ss . Please show the details of your derivation to earn points. Draw the Solow model graph showing the savings line and the depreciation line and marking the steady state level of k.

b) Now, consider the “AK model” with production function ?? = ???? , where A is the exogenous productivity level. Again, assume that there is no population growth in the economy. Follow the similar steps in part a. to derive the capital accumulation equation in terms of capital per capita ??.

c) Based on the equations you derived in part b, draw a graph similar to that of the Solow growth model to show the steady state of the model in part b. If you cannot find such a steady state, please explain why.

d) . Recall that Solow growth model implies convergence in capital per capita. Does the model in part b has this feature?

Solutions

Expert Solution

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

Consider the standard Solow growth model. Let productivity be denoted by A and let the production...
Consider the standard Solow growth model. Let productivity be denoted by A and let the production function be Y=AF(K,N). For simplicity, assume that there is no population growth (n=0 so that N'=N). Let depreciation be denoted by d and the savings rate by s. a. Derive the per capita capital accumulation equation for k=K/N and the steady state level of capital per worker, kss. Please show the details of your derivation to earn points. Draw the Solow model graph showing...
Let us consider a Solow growth model in which the aggregate production function at time t...
Let us consider a Solow growth model in which the aggregate production function at time t for country i is given by: Yit =Ai(Kit)1-βi(ei Lit) βi Where Yit is the aggregate real GDP in country i, Kit   is the aggregate physical capital in country i, Lit     is the aggregate number of workers in country i, ei is the average working time of a worker parameter in country i, Ai >0 is the total factor productivity parameter in country i and...
Let us consider a Solow growth model in which the aggregate production function at time t...
Let us consider a Solow growth model in which the aggregate production function at time t for country i is given by: Yit =Ai(Kit)1-βi(ei Lit) βi Where Yit is the aggregate real GDP in country i, Kit   is the aggregate physical capital in country i, Lit     is the aggregate number of workers in country i, ei is the average working time of a worker parameter in country i, Ai >0 is the total factor productivity parameter in country i and...
Consider the Solow Growth model, and assume there is no technological change. The production function is...
Consider the Solow Growth model, and assume there is no technological change. The production function is F(K,L) = K^aN^1−α, α = 1/3. Population growth rate n = 0.01. Capital depreciation δ = 0.09. Savings rate s = 0.4. (a) Write down the law of motion for capital per worker. (b) Compute the steady state capital per worker and output per worker. (c) Suppose a book called Let’s Party Like There is No Tomorrow reduces the nation’s savings rate to 0.35....
In the Solow growth model, if we assume the standard properties of the production technology, which...
In the Solow growth model, if we assume the standard properties of the production technology, which are discussed in class, the economy tends to move toward the steady state with positive capital stock per worker.
One of key predictions of the Solow Growth Model is that growth in total factor productivity...
One of key predictions of the Solow Growth Model is that growth in total factor productivity will ensure long run economic growth. While Canada has been making progress in terms of a growing technology sector due to many factors, some of which include: strong economic base and rising standard of living highly educated work force multi-cultural mix and friendly business environment universal health care foreign immigration policies friendly domestic immigration policy and foreign anti-immigration policies Discuss some public policies that...
One of key predictions of the Solow Growth Model is that growth in total factor productivity...
One of key predictions of the Solow Growth Model is that growth in total factor productivity will ensure long run economic growth. While Canada has been making progress in terms of a growing technology sector due to many factors, some of which include: strong economic base and rising standard of living highly educated work force multi-cultural mix and friendly business environment universal health care foreign immigration policies friendly domestic immigration policy and foreign anti-immigration policies Discuss three public policies (in...
2. Consider the Solow growth model. Suppose that the production function is constant returns to scale...
2. Consider the Solow growth model. Suppose that the production function is constant returns to scale and it is explicitly given by: Y = KaL1-a a. What is the level of output per capita, y, where y = Y/L? b. Individuals in this economy save s fraction of their income. If there is population growth, denoted by n, and capital depreciates at the rate of d over time, write down an equation for the evolution of capital per capita, k,...
2) Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters:...
2) Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters: α = 0.4; d = 0.05; A = 1; s = 0.75; n = 0.4 a) Calculate the rate of capital accumulation (law of motion) b) Calculate the steady state level of capital? c) Calculate the steady state level of real output/income? d) Calculate the steady state level of investment? e) Calculate the steady state level of consumption? f) What effect does a higher...
Consider the Solow growth model with population growth and growth in the efficiency of labor. Suppose...
Consider the Solow growth model with population growth and growth in the efficiency of labor. Suppose that 2 countries A and B have the same production function given by Yt = Ktα(LtEt)1−α, the same rate of growth of E (g), the same depreciation rate of physical capital (δ) and the same saving rate s. The initial level of E, E0, is lower in country A than in country B. (a) Compare the steady-state levels of output per effective worker of...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT