Production function calculations Equation:...

Description

New solution updates


Question

Production function calculations
Equation
Y = A*K^alpha*L^(1-alpha)
Problem 1: given inputs and productivity, find output
A=
2
K=
5
L=
10
alpha =
0.33333333
Answer
Y=
Problem 2: given inputs and output, find productivity
Y=
10
K=
20
L=
5
alpha =
0.33333333
Answer
A=
Solow model simulations
Idea: each date is connected to the previous one
Inputs (from Penn World Table)
Y0 =
4.0790 (initial GDP)
A0 =
3.4299 (initial TFP)
K0 =
8.2330 (initial capital)
L0 =
0.4520 (initial labor)
alpha =
0.3333 (capital share in production function)
s=
0.2500 (saving/investment rate)
delta =
0.0600 (deprec rate)
a=
0.0000 (TFP growth rate)
n=
0.0000 (labor growth rate)
Simulation
Date
TFP
Capital
Labor
GDP
2010
3.43
8.23
0.452
2011
3.43
8.76
0.452
2012
3.43
9.27
0.452
2013
3.43
9.78
0.452
2014
3.43
10.27
0.452
2015
3.43
10.75
0.452
2016
3.43
11.22
0.452
2017
3.43
11.68
0.452
2018
3.43
12.13
0.452
2019
3.43
12.56
0.452
2020
3.43
12.98
0.452
2021
3.43
13.39
0.452
2022
3.43
13.78
0.452
2023
3.43
14.17
0.452
2024
3.43
14.54
0.452
2025
3.43
14.90
0.452
2026
3.43
15.25
0.452
2027
3.43
15.58
0.452
2028
3.43
15.91
0.452
2029
3.43
16.23
0.452
2030
3.43
16.53
0.452
2031
3.43
16.83
0.452
2032
3.43
17.11
0.452
2033
3.43
17.39
0.452
2034
3.43
17.65
0.452
2035
3.43
17.91
0.452
2036
3.43
18.15
0.452
2037
3.43
18.39
0.452
2038
3.43
18.62
0.452
2039
3.43
18.84
0.452
2040
3.43
19.06
0.452
2041
3.43
19.26
0.452
2042
3.43
19.46
0.452
2043
3.43
19.65
0.452
2044
3.43
19.83
0.452
2045
3.43
20.01
0.452
2046
3.43
20.18
0.452
2047
3.43
20.35
0.452
2048
3.43
20.50
0.452
2049
3.43
20.66
0.452
2050
3.43
20.80
0.452
4.08
4.16
4.24
4.32
4.39
4.46
4.52
4.58
4.64
4.70
4.75
4.80
4.84
4.89
4.93
4.97
5.01
5.05
5.08
5.11
5.15
5.18
5.21
5.23
5.26
5.28
5.31
5.33
5.35
5.38
5.40
5.41
5.43
5.45
5.47
5.48
5.50
5.51
5.53
5.54
5.56
Sav=Inv Deprec
1.02
0.49
1.04
0.53
1.06
0.56
1.08
0.59
1.10
0.62
1.11
0.65
1.13
0.67
1.15
0.70
1.16
0.73
1.17
0.75
1.19
0.78
1.20
0.80
1.21
0.83
1.22
0.85
1.23
0.87
1.24
0.89
1.25
0.91
1.26
0.94
1.27
0.95
1.28
0.97
1.29
0.99
1.29
1.01
1.30
1.03
1.31
1.04
1.31
1.06
1.32
1.07
1.33
1.09
1.33
1.10
1.34
1.12
1.34
1.13
1.35
1.14
1.35
1.16
1.36
1.17
1.36
1.18
1.37
1.19
1.37
1.20
1.37
1.21
1.38
1.22
1.38
1.23
1.39
1.24
1.39
1.25

 

Solution ID:351101 | This paper was updated on 26-Nov-2015

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