Consider a model of the economy's aggregate output, where output in period t is given by:Y₁ = A+K (h+Lt) ¹-aWhere At is TFP in period t, K, is the capital stock, L, is the labor force, and he is the averageeducation of each worker.a) Use the growth accounting framework to find an expression for the growth rate of output. (hint,take the natural log of the expression and then a derivative with respect to time, t).b) Using the data in the table below, and your expression from part (a) above, calculate the growthrate in TFP. Assume that capital's share of income, a, is 1/3. (hint, to calculate the growth rate ina variable, say GDP, calculate the percentage change over the base year: gy =- Yt+1-Yt)Ytt20212022Y₁100.0105.0Kt15.015.5Lt10.010.1ht13.3013.44c) Based upon your calculations above, what is the share of growth in output that is attributable togrowth in TFP? Further, can we conclude that this represents the contribution of innovation toeconomic growth over this period? Why or why not? Explain.

Answered: Consider a model of the economy's…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a model of the economy's aggregate output, where output in period t is given by:
Y₁ = A+K (h+Lt) ¹-a
Where At is TFP in period t, K, is the capital stock, L, is the labor force, and he is the average
education of each worker.
a) Use the growth accounting framework to find an expression for the growth rate of output. (hint,
take the natural log of the expression and then a derivative with respect to time, t).
b) Using the data in the table below, and your expression from part (a) above, calculate the growth
rate in TFP. Assume that capital's share of income, a, is 1/3. (hint, to calculate the growth rate in
a variable, say GDP, calculate the percentage change over the base year: gy =
- Yt+1-Yt)
Yt
t
2021
2022
Y₁
100.0
105.0
Kt
15.0
15.5
Lt
10.0
10.1
ht
13.30
13.44
c) Based upon your calculations above, what is the share of growth in output that is attributable to
growth in TFP? Further, can we conclude that this represents the contribution of innovation to
economic growth over this period? Why or why not? Explain.

Expert Solution

Step 1

Given production function

$Y_{t} = A_{t} {K_{t}}^{α} {(h_{t} L_{t})}^{1 - α} A_{t} - - T o t a l f a c t o r p r o d u c t i v i t y h_{t} - - - a v e r a g e e d u c a t i o n L_{t} - - - L a b o r f o r c e K_{t} - - C a p i t a l P r o d u c t i o n f u n c t i o n c a n b e w r i t t e n a s Y_{t} = A_{t} {K_{t}}^{α} {h_{t}}^{1 - α} {L_{t}}^{1 - α}$

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