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.
This exercise is part of the course
Introduction to Optimization in Python
Exercise instructions
- Define the constraint as
mand generate the combinations ofcandm. - Define the utility function and assign it to
F. - Plot the contours and constraint.
Hands-on interactive exercise
Have a go at this exercise by completing this sample 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()