Question

Suppose that an economy has the per-worker production function given as: y = 345 where y is output per worker and kis capital per worker. In addition, national savings is given as: S, = 0.3Y where S is national savings and Y is total output Use the production and savings functions on your left and the depreciation and population growth rates below to answer the following questions. (Round all numerical responses to one decimal place.) Depreciation rate (d) = 0.1 Population growth rate (n) = 0.05 What is the steady-state value of the capital-labor ratio, K? 36 What is the steady-state value of output per worker, y? 18 What is the steady-state value of consumption per worker, c?

Answer 1

y = 3k s.y = (stgn)k 0.5 0+3 X34K = 0.15k Ik = 0.15k RE 0-5 - k = 36 capital labour rates 015 y = 3 xk a 3x6 y = 18 output per wooker, c = - - (1-6).Y C1-0.3).Y 0.7818 = 12.6 K Consumption per worker