In this simulation of the Solow Growth Model, you can see the long-run economic implications of changes in the saving rate, the population growth rate and shocks to the capital stock. You can change the initial steady state or introduce a shock to the economy. When you make a change, the computer calculates the new initial and final steady states, as well as the transition path between them.
The exogenous variables of the Solow Growth Model are
the rate of population growth (n), and
the rate of saving (s).
The endogenous variables are
the level of capital per worker (k), and
the level of output per worker (y).
The "steady state" is a long-run equilibrium in which the levels of y and k are constant. You can use the Solow model to find the steady-state levels of the endogenous variables and to describe the path along which the economy approaches the steady state if it does not start in steady state.
The model begins with a production function that expresses the level of output per worker as a function of the level of capital per worker:
y = f(k)
Higher levels of capital per worker produce higher levels of output per worker. The production function exhibits decreasing returns: that is, as k grows, its marginal product falls.
The second equation in the model describes how the capital stock changes over time:
change in k = s * f(k) - (n+delta) * k
The saving rate is s, so s * f(k) is the amount of output used to create new capital. Depreciation (delta) and population growth (n) reduce the amount of capital per worker.
In steady state, the change in k is equal to 0, implying
s * f(k) = (n+delta) * k
This steady state relationship is summarized in the textbook.
If the economy is out of steady state, the levels of output and capital per worker will gradually adjust to their new steady state levels, as is shown in figure 4-9 in the text.
In the computer simulation for this chapter, you will have the opportunity to examine both changes in the steady state and changes in output and consumption that occur along the transition to the steady state. You can set the levels of saving and population growth in an initial steady state (the two sliders on the left marked "Until 1999") and in a final steady state (the two sliders on the right marked "2000+").
Changing the parameters will affect both the initial steady state and the steady state after 2000.
Initially, a graph of y (output per capita) and c (consumption per capita) appears. To see a table of the endogenous variables instead, click on the main tab named "Table." The table shows the paths of capital per capita, output per capita, consumption per capita, investment per capita, depreciation, and the marginal product of capital (MPK) from 1999 to 2074. Use the up and down arrows to scroll through the table. The last row of the table shows the new steady state values.
Year | Capital | Output | Consump | Invest | Deprec | MPK |
---|---|---|---|---|---|---|
2004 | 6.25 | 2.50 | 2.13 | 0.37 | 0.31 | 0.200 |
2005 | 6.31 | 2.51 | 2.13 | 0.38 | 0.32 | 0.199 |
2006 | 6.37 | 2.52 | 2.14 | 0.38 | 0.32 | 0.198 |
2007 | 6.25 | 2.50 | 2.13 | 0.37 | 0.31 | 0.200 |
2008 | 6.31 | 2.51 | 2.13 | 0.38 | 0.32 | 0.199 |
2009 | 6.37 | 2.52 | 2.14 | 0.38 | 0.32 | 0.198 |
2010 | 6.43 | 2.54 | 2.16 | 0.38 | 0.32 | 0.198 |
2011 | 6.49 | 2.55 | 2.17 | 0.38 | 0.32 | 0.196 |
2012 | 6.55 | 2.56 | 2.18 | 0.38 | 0.33 | 0.195 |
2013 | 6.60 | 2.57 | 2.18 | 0.39 | 0.33 | 0.195 |
2014 | 6.66 | 2.58 | 2.19 | 0.39 | 0.33 | 0.194 |
2015 | 6.72 | 2.59 | 2.20 | 0.39 | 0.34 | 0.193 |
2016 | 6.77 | 2.60 | 2.21 | 0.39 | 0.34 | 0.192 |
2017 | 6.82 | 2.61 | 2.22 | 0.39 | 0.34 | 0.191 |
2018 | 6.87 | 2.62 | 2.23 | 0.39 | 0.34 | 0.191 |
2019 | 6.92 | 2.63 | 2.24 | 0.39 | 0.35 | 0.190 |
2020 | 6.96 | 2.64 | 2.24 | 0.40 | 0.35 | 0.190 |
2021 | 7.01 | 2.65 | 2.25 | 0.40 | 0.35 | 0.189 |
2022 | 7.06 | 2.66 | 2.26 | 0.40 | 0.35 | 0.188 |
2023 | 7.11 | 2.67 | 2.27 | 0.40 | 0.36 | 0.188 |
2024 | 7.15 | 2.67 | 2.27 | 0.40 | 0.36 | 0.187 |
2025 | 7.19 | 2.68 | 2.28 | 0.40 | 0.36 | 0.186 |
2026 | 7.23 | 2.69 | 2.29 | 0.40 | 0.36 | 0.186 |
2027 | 7.27 | 2.70 | 2.29 | 0.41 | 0.36 | 0.186 |
2028 | 7.32 | 2.71 | 2.30 | 0.41 | 0.37 | 0.185 |
2029 | 7.36 | 2.71 | 2.30 | 0.41 | 0.37 | 0.184 |
2030 | 7.40 | 2.72 | 2.31 | 0.41 | 0.37 | 0.184 |
2031 | 7.44 | 2.73 | 2.32 | 0.41 | 0.37 | 0.183 |
2032 | 7.48 | 2.73 | 2.32 | 0.41 | 0.37 | 0.182 |
2033 | 7.52 | 2.74 | 2.33 | 0.41 | 0.38 | 0.182 |
2034 | 7.55 | 2.75 | 2.34 | 0.41 | 0.38 | 0.182 |
2035 | 7.58 | 2.75 | 2.34 | 0.41 | 0.38 | 0.181 |
2036 | 7.61 | 2.76 | 2.35 | 0.41 | 0.38 | 0.181 |
2037 | 7.64 | 2.76 | 2.35 | 0.41 | 0.38 | 0.181 |
2038 | 7.67 | 2.77 | 2.35 | 0.42 | 0.38 | 0.181 |
2039 | 7.71 | 2.78 | 2.36 | 0.42 | 0.39 | 0.180 |
2040 | 7.74 | 2.78 | 2.36 | 0.42 | 0.39 | 0.180 |
2041 | 7.77 | 2.79 | 2.37 | 0.42 | 0.39 | 0.180 |
2042 | 7.80 | 2.79 | 2.37 | 0.42 | 0.39 | 0.179 |
2043 | 7.83 | 2.80 | 2.38 | 0.42 | 0.39 | 0.179 |
2044 | 7.86 | 2.80 | 2.38 | 0.42 | 0.39 | 0.178 |
2045 | 7.89 | 2.81 | 2.39 | 0.42 | 0.39 | 0.178 |
2046 | 7.92 | 2.81 | 2.39 | 0.42 | 0.40 | 0.177 |
2047 | 7.94 | 2.82 | 2.40 | 0.42 | 0.40 | 0.178 |
2048 | 7.96 | 2.82 | 2.40 | 0.42 | 0.40 | 0.177 |
2049 | 7.98 | 2.82 | 2.40 | 0.42 | 0.40 | 0.177 |
2050 | 8.00 | 2.83 | 2.41 | 0.42 | 0.40 | 0.177 |
2051 | 8.02 | 2.83 | 2.41 | 0.42 | 0.40 | 0.176 |
2052 | 8.04 | 2.84 | 2.41 | 0.43 | 0.40 | 0.177 |
2053 | 8.07 | 2.84 | 2.41 | 0.43 | 0.40 | 0.176 |
2054 | 8.10 | 2.85 | 2.42 | 0.43 | 0.41 | 0.176 |
2055 | 8.12 | 2.85 | 2.42 | 0.43 | 0.41 | 0.175 |
2056 | 8.14 | 2.85 | 2.42 | 0.43 | 0.41 | 0.175 |
2057 | 8.16 | 2.86 | 2.43 | 0.43 | 0.41 | 0.175 |
2058 | 8.18 | 2.86 | 2.43 | 0.43 | 0.41 | 0.175 |
2059 | 8.20 | 2.86 | 2.43 | 0.43 | 0.41 | 0.174 |
2060 | 8.22 | 2.87 | 2.44 | 0.43 | 0.41 | 0.175 |
2061 | 8.24 | 2.87 | 2.44 | 0.43 | 0.41 | 0.174 |
2062 | 8.26 | 2.87 | 2.44 | 0.43 | 0.41 | 0.174 |
2063 | 8.28 | 2.88 | 2.45 | 0.43 | 0.41 | 0.174 |
2064 | 8.30 | 2.88 | 2.45 | 0.43 | 0.42 | 0.173 |
2065 | 8.31 | 2.88 | 2.45 | 0.43 | 0.42 | 0.173 |
2066 | 8.32 | 2.88 | 2.45 | 0.43 | 0.42 | 0.173 |
2067 | 8.33 | 2.89 | 2.46 | 0.43 | 0.42 | 0.173 |
2068 | 8.34 | 2.89 | 2.46 | 0.43 | 0.42 | 0.173 |
2069 | 8.35 | 2.89 | 2.46 | 0.43 | 0.42 | 0.173 |
2070 | 8.36 | 2.89 | 2.46 | 0.43 | 0.42 | 0.173 |
2071 | 8.37 | 2.89 | 2.46 | 0.43 | 0.42 | 0.173 |
2072 | 8.38 | 2.89 | 2.46 | 0.43 | 0.42 | 0.172 |
2073 | 8.39 | 2.90 | 2.46 | 0.44 | 0.42 | 0.173 |
2074 | 8.41 | 2.90 | 2.46 | 0.44 | 0.42 | 0.172 |
2075 | 8.43 | 2.90 | 2.46 | 0.44 | 0.42 | 0.172 |
2076 | 8.45 | 2.91 | 2.47 | 0.44 | 0.42 | 0.172 |