This exercise illustrates the classical utility maximization problem using Cobb-Douglas preferences under a linear budget constraint. Given prices and income, we derive the optimal consumption bundle analytically and graphically. The plot displays:
The budget constraint (RO),
Three indifference curves (U₁, U₂, U₃) with varying utility levels,
The interior solution where the highest attainable indifference curve is tangent to the budget line,
Dashed lines projecting the optimal bundle onto the axes,
Axis labels highlighting the optimal quantities.
The code is written in R using ggplot2, and is fully reproducible and easily extendable to other preference specifications.
