P3 1. Let's assume that a country - the Kingdom of Hogwarts - grows, by some magic, exactlyfollowing the Solow growth model. The country has a Cobb-Douglas production function suchasY = AK0.5 L0.5.In this economy, the fraction of output invested (saved), s, is equal to 0.25, annual growth rateof population (labor force) is 0.02, and the depreciation rate of the capital stock is 0.03 peryear.(1) Assume that there is no technology progress, and the level of technology (A) is always equalto one. Suppose that this economy's initial capital stock per capita (labor) (k =) at the%3Dyear t=0 is equal to 4. Calculate the economy's per capita capital stock, per capita output,and growth rates of per capita capital and output at the year t=1 and at the steady state.Explain how they change over time graphically.(2) Assume all of sudden the investment rate, s, increases to 0.5, with all other conditions beingthe same as the country in (1). Calculate steady-state levels for capital and output per capita.(3) Compare two different steady states between low saving rate (0.25) and high saving rate(0.5). Which one do you think is better? Let's assume that the “best" steady state has thehighest possible consumption per person in the steady state: c* = (1 – s)Aƒ (k*). Whydoesn’t a higher saving rate necessarily lead to a better steady state?

given that, Cobb-Douglas production function such as, Y = AK0.5L0.5

Let's assume that a country - the Kingdom of Hogwarts - grows following the Solow growth model. The country has a Cobb-Dougla as Y = AKO.5L0.5. In this economy, the fraction of output invested (saved), s, is equal t

Let's assume that a country - the Kingdom of Hogwarts - grows following the Solow growth model. The country has a Cobb-Dougla as Y = AKO.5L0.5. In this economy, the fraction of output invested (saved), s, is equal t

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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