# Interactive Cobb-Douglas Utility Function

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”