This document describes a country's production function and saving function to analyze its long-run economic growth. It asks questions about deriving the steady-state values of capital-labor ratio and outputs, showing the results on a Solow diagram, determining the balanced growth rates of total output and capital, explaining the difference between capital deepening and widening, and whether the model can generate sustained per capita income growth.

1. A country has the following per-worker production function yt=5kt0.5 Where yt is output per
worker and kt is the capital-labor ratio. The depreciation rate is 0.2 and the population growth
rate is 0.05 . The saving function isSt=0.2Yt Where St it the total national saving and Yt is total
output. 1.1 Derive the steady-state values of the capital-labor ratio, output per worker,
consumption per worker, and investment per worker? 1.2 Show your results on the Solow
diagram. 1.3 What is the long-run balanced growth in total output and capital? 1.4 What is the
long-run balanced growth in output per worker and capital per worker? 1.5 Explain the
difference between capital deepening and capital widening. 1.6 Suppose the economy begins
with a level of k less than k. As k moves toward k, is w (a wage for each unit of labor) growing
at a rate greater than, less than, or equal to its growth rate on the balanced growth path? 1.7 Can
this model generate sustained economic growth in per capita income? Explain.