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Visualize the indifference curve

You have been provided the following utility function and constraint.

\(U(c, m)=c^{0.7}m^{0.3}\)

\(c+m=2\)

Use this to visualize the indifference curve.

np and plt have been loaded for you.

Cet exercice fait partie du cours

Introduction to Optimization in Python

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Instructions

  • Define the constraint as m and generate the combinations of c and m.
  • Define the utility function and assign it to F.
  • Plot the contours and constraint.

Exercice interactif pratique

Essayez cet exercice en complétant cet exemple de code.

c = np.linspace(1, 2, 10)  
# Define the constraint and generate combinations
m = ____
C, M = ____(c, m)
# Define the utility function
F = ____

plt.figure(figsize=(8, 6))
# Plot the controls and constraints
contours = ____(C, M, F, levels=[0.9, 1.00, 1.085, 1.2])
____(contours)
____(c, m, color='red')
plt.title('Indifference Curve with Constraint Line')
plt.xlabel('c')
plt.ylabel('m')
plt.grid(True)
plt.show()
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