Suppose the production function is given by Y= VK\N, where Y is the amount of output, K is the amount of capital, and N is the number of workers. Suppose further that there are no technological progress and population growth. What is the expression in terms of the saving rate, s, and the depreciation rate, 8, for the level of consumption per worker in the steady state?

Consider an economy that exhibits both population growth (L grows at rate n) and technological progress (A grows at rate a) described by the production function, Y = F(K,AL) = Kª(AL)¹-α| Here K is capital and Y is output. (a) Show that this production function exhibits constant returns to scale. What is the per-effective-worker production function? (c) Find expressions for the steady-state capital-output ratio, capital stock per effective worker, and output per effective worker, as a function of the saving rate (s), the depreciation rate (8), the population growth rate (n), the rate of technological progress (a), and the coefficient a. (You may assume the condition that capital per effective worker evolves according to Ak = sf (k) − (a +n+8)k.) (d) Show that at the Golden Rule steady state the saving rate for this economy is equal to the parameter a.

if real GDP grows at an annual rate of 3.4% and the population grows at an annual rate of 1.6% then at approximately what rate is the real GDP per capital growing?

9. Suppose there is no population or technological growth. Define k as the capital-to-labor ratio. If the per worker production function is given by y = ¹/2, the saving ratio is 0.3, and the depreciation rate is 0.1, then the steady state capital per worker ratio is (a) 1 (b) 2 (c) 4 (d) 6 9