Question
Suppose that the production function is Y = zK^1/2N^1/2 and that 7% of capital wears out every year. Assume that the rate of growth of
Suppose that the production function is Y = zK^1/2N^1/2 and that 7% of capital wears out every year. Assume that the rate of growth of the population is 3% and the saving rate is 15%. The productivity level is z = 2.
(d) What is the steady-state growth rate of the capital per worker, kss, and the steady-state growth rate of the output per worker, yss? \
(e) What is the steady-state growth rate of the capital stock, Kss, and the steady-state growth rate of the aggregate output, Yss? Show your work.
(f ) The government is benevolent (cares about the consumers) and wants to maximize the steady state consumption per worker. Write down the maximization problem that the golden rule capital per worker, k*gr, solves. Find k*gr.
(g) What is the savings rate associated with the golden rule level of capital, s*gr? Can the country increase the consumption per-capita by changing the saving rate?
(h) Now assume that there is no population growth, i.e. n = 0, and that the saving rate is given by some other value called s . Suppose that this economy is in a steady state where the marginal product of capital is less than the depreciation rate. By changing the saving rate is it possible to increase the steady state consumption per-capita? Explain how would you change the saving rate.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started