The Cobb-Douglas utility function is a commonly used functional form to model consumer behavior.

The Cobb-Douglas utility function takes the general form

\[U(x,y) = x^a \cdot y^b\]

Through the ShinyApp provided below, users can interactively explore two Cobb-Douglas utility functions for two goods, namely x and y. The blue line depicts the first budget and utility function, while the red line represents the second budget and utility function.

By utilizing the budget widget, users can set the first budget constraint. The second widget, budget (new), enables the selection of the second budget. Additionally, users can manipulate the prices of both goods, x and y, through the Price X and Price Y functions.

The alpha and beta widgets, let you play with the \(a\) and \(b\) of the utility function (\(x^a \cdot y^b\)).

The table below the Figure gives you the optimal choice given the Budget.

You can find the ShinyApp here: https://giacomovagni.shinyapps.io/cobbs_douglas/

For more information about the Cobb-Douglas function see Hal R. Varian “Intermediate Microeconomics, A Modern Approach Eighth Edition”