A country has the following per-worker production function Yt = 5k0.5 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 is St = 0.2Yt Where St it the total national saving and Y, is total output. 1.1 What is the long-run balanced growth in output per worker and capital per worker? 1.2 Explain the difference between capital deepening and capital widening.

A country has the following per-worker production function Yt = 5k0.5 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 is St = 0.2Yt Where St it the total national saving and Y, is total output. 1.1 What is the long-run balanced growth in output per worker and capital per worker? 1.2 Explain the difference between capital deepening and capital widening.

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter20: Economic Growth In The Global Economy

Section: Chapter Questions

Problem 4P

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5. Suppose that the Country of Eldesarrollo has a gross savings rate of 25%, a depreciation rate of 3%, an incremental capital-output ratio of 2.75, a population growth rate of 1.5% per year, and a per capita income of $1500. a. Using the Harrod-Domar (or AK) growth model, calculate the implied rate of growth of total GNI in Eldesarrollo. b. What is the implied rate of growth of GNI per capita? c. How much would the rate of gross savings have to increase to raise the growth rate of total GNI to 9%? d. Suppose that one-quarter of all investment is completely wasted in Eldesarrollo. Returning to the original numbers, what is the resulting effective ICOR, and what is the corresponding new implied growth rate of total GNI?
Assume that a country's per-worker production is y = k1/2, where y is output per worker and kis capital per worker. Assume also that 10 percent of capital depreciates per year (= 0.10) 2 andthere is no population growth or technological change.a. If the saving rate (s) is 0.4, what are capital per worker, production per worker, andconsumption per worker in the steady state?b. Solve for steady-state capital per worker, production per worker, and consumption perworker with s = 0.6.c. Solve for steady-state capital per worker, production per worker, and consumption perworker with s = 0.8.d. Is it possible to save too much? Why?
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Question 2 A country has the following per-worker production function Yt = 5k0.5 Where yt is output per worker and kɩ is the capital-labor ratio. The depreciation rate is 0.2 and the population growth rate is 0.05. The saving function is St = 0.2Yt Where S, it the total national saving and Y, 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…
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4.If population growth rate is 0.03, and the depreciation rate is 0.2, then in order to maintain the steady state capital-labor ratio equal to the amount found in Qs. 2, what would be the investment per worker?
E1 Which of the following policies would likely increase productivity all else the same? A increasing legal rights for property owners B increasing in taxes on foreign portfolio investment C decreasing spending on education D decreasing spending on research and development