my_square = lambda x: x**2

my_square(4)

my_square(9)

def my_square_fn(x): ''' This function take an input x and return x^2. Parameters: ----------- x: float, integer or any other number Returns: -------- out = x**2 Example: >>> out = my_square_fn(4) >>> out 16 ''' return x**2

my_square_fn(4)

my_square_fn?

list(range(2, 20, 3))

print('The square of 100 is', my_square(100)) print('The square of 100 is ' + str(my_square(100)))

type([1, 'a', 3])

import os

os.getenv('HOME')

os.path.exists('pics')

pathout = './data' if os.path.exists(pathout) == False: os.mkdir(pathout)

from IPython.display import IFrame url = "https://ourworldindata.org" IFrame(url, width="100%", height="600px")

from IPython.display import IFrame url = "https://ourworldindata.org/grapher/countries-democracies-autocracies-row" IFrame(url, width="100%", height="600px")

from IPython.display import YouTubeVideo # Replace 'youtube_video_id' with the actual YouTube video ID youtube_video_id = 'WSKi8HfcxEk?si=zlRPlhGHPq1cOnte' # Create a YouTubeVideo object youtube_video = YouTubeVideo(youtube_video_id, width=800, height=600) # Display the YouTube video youtube_video

import matplotlib as mpl import matplotlib.pyplot as plt %matplotlib inline

x = [0, 1, 2, 3] y = [my_square(i) for i in x] plt.plot(x, y, c='r', marker='o', linestyle=':', label=r'$y=x^2$') plt.legend() plt.show()

x = [i/10 for i in range(0, 100)] y = [i**2 for i in x] z = [100 - 1/4 * i**2 + i for i in x]

fig, ax = plt.subplots(figsize=(8,5)) ax.plot(x, y, c='r', marker='o', markersize=4, linestyle='-.', label=r'$y=x^2$') ax.plot(x, z, c='b', marker='D', markersize=4, linestyle='-', label=r'$y=100-\frac{1}{4}x^2 + x$') ax.set_xlabel(r'$x$', fontsize=18) ax.set_ylabel(r'Value', fontsize=18) ax.set_title(r'Some Plots', fontsize=24) ax.legend(fontsize=18) plt.savefig('./pics/some-plots.png') plt.savefig('./pics/some-plots.pdf') plt.show()

import numpy as np

c = [1, 2] d = [[1, 2], [3, 4]] ca = np.array(c) da = np.array(d)

ca

da

ca**2

da * 3

ca*da

print(ca.shape) print(da.shape)

print('da=', da) print('Sum of all elements da.sum()=', da.sum()) print('Sum of all elements in each column da.sum(axis=0)=', da.sum(axis=0)) print('Sum of all elements in each row da.sum(axis=1)=', da.sum(axis=1)) print('dot product is ca.dot(da)=', ca.dot(da))

print(np.ones((3,4))) print(np.zeros((2,2))) print(np.eye(2)) print(np.ones_like(ca))

np.random.uniform(-1,1,10)

np.random.normal(10, 1, size=(3,3))

#np.random.seed(123456) x0 = 0 x = [x0] [x.append(x[-1] + np.random.normal() ) for i in range(500)] fig, ax = plt.subplots(figsize=(8,5)) ax.plot(x) plt.title(r'A simple random walk', fontsize=24) plt.xlabel(r'Period $t$', fontsize=18) plt.ylabel(r'$x_t$', fontsize=18) plt.show()

def cobb_douglas_output(A, K, L, alpha): output = A * (K ** alpha) * (L ** (1 - alpha)) return output A = 1.0 K = 1000.0 L = 500.0 alpha = 0.7 output_level = cobb_douglas_output(A, K, L, alpha) print("Output level:", output_level)

import numpy as np import matplotlib.pyplot as plt def cobb_douglas_output(A, K, L, alpha): output = A * (K ** alpha) * (L ** (1 - alpha)) return output A = 1.0 L = 1.0 K_values = np.linspace(0, 5, 100) output_values = cobb_douglas_output(A, K_values, L, 0.5) plt.figure(figsize=(8, 6)) plt.plot(K_values, output_values, label='Cobb-Douglas Production Function') plt.xlabel('Capital Input (K)') plt.ylabel('Output') plt.title('Cobb-Douglas Production Function') plt.legend() plt.grid(True) plt.show()

import numpy as np import matplotlib.pyplot as plt def cobb_douglas_output(A, K, L, alpha): output = A * (K ** alpha) * (L ** (1 - alpha)) return output L = 1.0 alpha = 0.5 K_values = np.linspace(0, 5, 100) A_values = [1, 2, 4, 5] plt.figure(figsize=(8, 6)) for A in A_values: output_values = cobb_douglas_output(A, K_values, L, alpha) plt.plot(K_values, output_values, label=f'A = {A}') plt.xlabel('Capital Input (K)') plt.ylabel('Output') plt.title('Effect of Increasing A on Cobb-Douglas Production Function') plt.legend() plt.grid(True) plt.show()

import numpy as np import matplotlib.pyplot as plt def cobb_douglas_output(A, K, L, alpha): output = A * (K ** alpha) * (L ** (1 - alpha)) return output K = 1.0 alpha = 0.5 L_values = np.linspace(1, 5, 100) A_values = [1, 2, 4, 5] plt.figure(figsize=(8, 6)) for A in A_values: output_values = cobb_douglas_output(A, K, L_values, alpha) plt.plot(L_values, output_values, label=f'A = {A}') plt.xlabel('Labor Input (L)') plt.ylabel('Output') plt.title('Effect of Increasing L on Cobb-Douglas Production Function') plt.legend() plt.grid(True) plt.show()

import numpy as np import matplotlib.pyplot as plt def cobb_douglas_output(A, K, L, alpha): output = A * (K ** alpha) * (L ** (1 - alpha)) return output alpha = 0.5 # Generate an array of K and L values from 0 to 5 with 100 points K_values = np.linspace(0, 5, 100) L_values = np.linspace(1, 5, 100) A_values = [1, 2, 4, 5] plt.figure(figsize=(12, 6)) plt.subplot(1, 2, 1) for A in A_values: output_values = cobb_douglas_output(A, K_values, L, alpha) plt.plot(K_values, output_values, label=f'A = {A}') plt.xlabel('Capital Input (K)') plt.ylabel('Output') plt.title('Effect of Increasing A on Cobb-Douglas Production Function') plt.legend() plt.grid(True) plt.subplot(1, 2, 2) for A in A_values: output_values = cobb_douglas_output(A, K, L_values, alpha) plt.plot(L_values, output_values, label=f'A = {A}') plt.xlabel('Labor Input (L)') plt.ylabel('Output') plt.title('Effect of Increasing L on Cobb-Douglas Production Function') plt.legend() plt.grid(True) plt.savefig('cobb_douglas_combined_plot.png') plt.savefig('cobb_douglas_combined_plot.jpg') plt.savefig('cobb_douglas_combined_plot.pdf') plt.tight_layout() plt.show()

from IPython.display import IFrame url = "https://fred.stlouisfed.org/searchresults?st=unemployment+by+city" IFrame(url, width="100%", height="600px")

from IPython.display import IFrame url = "https://databank.worldbank.org/source/world-development-indicators#" IFrame(url, width="100%", height="600px")