# Solow-Model with human capital and distorting taxation

**Importing relevant packages and modules**


```python
import numpy as np
from scipy import optimize
import sympy as sm
import matplotlib.pyplot as plt

# autoreload modules when code is run
%load_ext autoreload
%autoreload 2
#XD FOR SMART UPLOAD
# local modules
# import modelproject if code is used form another notebook or file
```

# Model description

The following solow-model incorperates human capital accumulation aswell as distorting taxation.

The model consists of the following equations:

1 $$ (1-\tau)^{\eta}L_t, \text{   } 0<\eta<1,$$
2 $$H_{t+1}={\tau}w_tN_t+(1-{\delta})H_t $$
3 $$K_{t+1}=s_kY_t+(1-{\delta})K_t $$
4 $$K^\alpha_{t}H^\beta_{t}(A_{t}N_{t})^{1-\alpha-\beta} $$
5 $$H_t=h_{t}N_t $$
6 $$L_{t+1}=(1+n)L_t $$
7 $$A_{t+1}=(1+g)A_t $$


* $K_t$ is capital in period t
* $L_t$ is labor i period t (with a constant growth rate of $n$)
* $H_t$ is human capital in period t
* $A_t$ is technology in period t (with a constant growth rate of $g$)
* $N_t$ is the total workhours supplied in the economy in period t
* $Y_t$ is GDP

The model contains the following parameters:$$(\eta,\tau,s_k,\delta,\alpha,\beta,n,g) $$

Using the equations above, we can find the two transitioncurves given by:
$$ \tilde{k}_{t+1}=\left(\frac{1}{(1+n)(1+g}\right)[s_{k}\tilde{k}^{\alpha}_{t}\tilde{h}^{\beta}_{t}(1-\tau)^{\eta(1+\alpha)}+(1+\delta)\tilde{k}_{t}] $$
and
$$ \tilde{h}_{t+1}=\left(\frac{1}{(1+n)(1+g}\right)[\tau(1-\alpha)\tilde{k}^{\alpha}_{t}\tilde{h}^{\beta}_{t}(1-\tau)^{\eta(1+\alpha)}+(1+\delta)\tilde{h}_{t}] $$
where $\tilde{k}_{t}$ is the capital per effective worker given by $\tilde{k}_{t}=\frac{Y}{AK}$
and
$\tilde{h}_{t}$ is the human capital per effective worker given by $\tilde{h}_{t}=\frac{Y}{AK}$


```python

```

0743b150557771d07131064fff02b058a3a02082
ipynb
Jupyter Notebook
modelproject/modelproject_working.ipynb
Santesson97/projects-2020-qvk188-og-sqn417
176f9648675e0d742083eaf621b28dc150f3071a
MIT
modelproject/modelproject_working.ipynb
Santesson97/projects-2020-qvk188-og-sqn417
176f9648675e0d742083eaf621b28dc150f3071a
MIT
modelproject/modelproject_working.ipynb
Santesson97/projects-2020-qvk188-og-sqn417
176f9648675e0d742083eaf621b28dc150f3071a
MIT
Qwen/Qwen-72B
1. YES
2. YES