1. O LounchPad • Country A and country B bothhave the production functionY = F(K, L) = K/³L²/3.a. Does this production function have constantreturns to scale? Explain.b. What is the per-worker production function,y = f(k)?c. Assume that neither country experiencespopulation growth or technological progressand that 20 percent of capital depreciates eachyear. Assume further that country A saves10 percent of output each year and countryB saves 30 percent of output each year. Usingyour answer from part (b) and the steady-statecondition that investment equals depreciation,find the steady-state level of capital per work-er for each country. Then find the steady-statelevels of income per worker and consumptionper worker.d. Suppose that both countries start off with acapital stock per worker of 1. What are thelevels of income per worker and consumptionper worker?

A production function has constant return to scale if the inputs and the outputs change by the…

Answered: O LounchPad • Country A and country B…

O LounchPad • Country A and country B both have the production function Y = F(K, L) = K/³L?/3. %3D a. Does this production function have constant returns to scale? Explain.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

1. O LounchPad • Country A and country B both
have the production function
Y = F(K, L) = K/³L²/3.
a. Does this production function have constant
returns to scale? Explain.
b. What is the per-worker production function,
y = f(k)?
c. Assume that neither country experiences
population growth or technological progress
and that 20 percent of capital depreciates each
year. Assume further that country A saves
10 percent of output each year and country
B saves 30 percent of output each year. Using
your answer from part (b) and the steady-state
condition that investment equals depreciation,
find the steady-state level of capital per work-
er for each country. Then find the steady-state
levels of income per worker and consumption
per worker.
d. Suppose that both countries start off with a
capital stock per worker of 1. What are the
levels of income per worker and consumption
per worker?

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