%%javascript

IPython.OutputArea.prototype._should_scroll = function(lines) {
    return false;
}

# KEEP GRAPHICS IN THE MAIN NOTEBOOK FLOW

%matplotlib inline 

# GRAPHICS SETUP 
#
# seaborn-whitegrid styles and figure size...

from matplotlib import pyplot as plt

plt.style.use('seaborn-whitegrid')

figure_size = plt.rcParams["figure.figsize"]
figure_size[0] = 10
figure_size[1] = 7
plt.rcParams["figure.figsize"] = figure_size

# IMPORT LIBRARIES...

import numpy as np
import pandas as pd

# DEFINE OUR SOLOW GROWTH MODEL SIMULATION FUNCTION...
#
# we are going to want to see what happens for lots of
# different model parameter values and initial conditions,
# so stuff everything inside a function, so we can then
# invoke it with a single line...

def sgm_2_200yr_run(L0, E0, 
    n=0, g=0, s=0.15, 
    alpha=0.5, delta=0.025, 
    delta_n = 0, delta_g = 0, delta_s = 0, 
    T = 200):

    sg_df = pd.DataFrame(index=range(T),columns=['Labor', 
        'Efficiency',
        'Capital',
        'Output',
        'Output_per_Worker',
        'Capital_Output_Ratio'],
        dtype='float')

    sg_df.Labor[0] = L0
    sg_df.Efficiency[0] = E0
    sg_df.Capital_Output_Ratio[0] = s/(n+g+delta)
    sg_df.Output[0] = sg_df.Capital_Output_Ratio[0]**(alpha/(1-alpha)) * sg_df.Labor[0] * sg_df.Efficiency[0]
    sg_df.Output_per_Worker[0] = sg_df.Output[0]/sg_df.Labor[0]
    sg_df.Capital = sg_df.Capital_Output_Ratio[0] * sg_df.Output[0]
    
    s = s + delta_s
    g = g + delta_g
    n = n + delta_n

    for i in range(T):
        sg_df.Labor[i+1] = sg_df.Labor[i] + sg_df.Labor[i] * n
        sg_df.Efficiency[i+1] = sg_df.Efficiency[i] + sg_df.Efficiency[i] * g
        sg_df.Capital[i+1] = sg_df.Capital[i] - sg_df.Capital[i] * delta + sg_df.Output[i] * s 
        sg_df.Output[i+1] = (sg_df.Capital[i+1]**alpha * (sg_df.Labor[i+1] * sg_df.Efficiency[i+1])**(1-alpha))
        sg_df.Output_per_Worker[i+1] = sg_df.Output[i+1]/sg_df.Labor[i+1]
        sg_df.Capital_Output_Ratio[i+1] = sg_df.Capital[i+1]/sg_df.Output[i+1]

        
    fig = plt.figure(figsize=(12, 12))

    ax1 = plt.subplot(2,3,1)
    sg_df.Labor.plot(ax = ax1, title = "Labor Force")
    plt.ylabel("Values")

    ax2 = plt.subplot(2,3,2)
    sg_df.Efficiency.plot(ax = ax2, title = "Efficiency of Labor")

    ax3 = plt.subplot(2,3,3)
    sg_df.Capital.plot(ax = ax3, title = "Capital Stock")

    ax4 = plt.subplot(2,3,4)
    sg_df.Output.plot(ax = ax4, title = "Output")
    plt.ylabel("Values")
    plt.xlabel("Years")

    ax5 = plt.subplot(2,3,5)
    sg_df.Output_per_Worker.plot(ax = ax5, title = "Output per Worker")
    plt.xlabel("Years")

    ax6 = plt.subplot(2,3,6)
    sg_df.Capital_Output_Ratio.plot(ax = ax6, title = "Capital-Output Ratio")
    plt.xlabel("Years")

    plt.suptitle('Solow Growth Model: Simulation Run', size = 20)

    plt.show()

    print(alpha, "is the orientation-of-growth-toward-capital parameter: alpha")
    print(delta, "is the depreciation rate: delta")

    if (delta_n != 0):
        print(n, "is the alternative labor-force growth rate: n'")
        print(n - delta_n, "is the baseline labor-force growth rate: n")        
    else:
        print(n, "is the labor force growth rate: n")
    
    if (delta_g != 0):
        print(g, "is the alternative efficiency-of-labor growth rate: g'")
        print(g - delta_g, "is the baseline efficiency-of-labor growth rate: g")                
    else:
        print(g, "is the efficiency of labor growth rate: g")
    
    if (delta_s != 0):
        print(s, "is the alternative post-jump savings-investment share: s'")
        print(s - delta_s, "is the baseline pre-jump savings-investment share: s")
    else:
        print(s, "is the savings-investment share: s")

print("Function creation ran without visible errors")

# start with a model with no labor force or
# efficiency of labor growth...

sgm_2_200yr_run(L0 = 1000, E0 = 1, g = 0, n = 0,
    s = 0.15, delta_s = 0.03)

# it works in reverse...
#
# start with a model with no labor force or
# efficiency of labor growth...

sgm_2_200yr_run(L0 = 1000, E0 = 1, g = 0, n = 0,
    s = 0.15, delta_s = -0.03)

# Add in labor-force growth

sgm_2_200yr_run(L0 = 1000, E0 = 1, g = 0, n = 0.015,
    s = 0.15, delta_s = 0.03, T=200)

# Add in efficiency-of-labor growth

sgm_2_200yr_run(L0 = 1000, E0 = 0.1, g = 0.02, n = 0.015,
    s = 0.15, delta_s = 0.03, T=200)

sgm_2_200yr_run(L0 = 1000, E0 = 1, g = 0.015, n = 0.01,
    s = 0.16, delta_s = 0.04, T=100)