Cobb-Douglas Utility Function Calculator - Utility Maximization Problem



Cobb-Douglas Utility Function Calculator - Utility Maximization Problem helps solving the Utility maximization problem given Cobb-Douglas Utility Function

What is Cobb-Douglas Utility Function?

In economics, an utility function is a functional representation of consumer preferences.

The Cobb-Douglas utility function is a particular form of the utility function. It is widely used because it has many attractive characteristics.

The Formula of Cobb-Douglas Utility Function

The basic form of the Cobb-Douglas Utility function is as follows:

U(x,y) = A x^α y^β

Where:

U is the utility from consuming x units of the first product and y units of the seocnd product.

A is a positive constant.

x is the quantity of product 1.

y is the quantity of product 2.

α is the utility elasticity of product 1.

β is the utility elasticity of product 2.

α and β are constants between 0 and 1.

The positive constant (A)

The utility elasticity of product 1 (α)

The utility elasticity of product 2 (β)

Per unit cost of Product 1 (P_x) Dollars

Per unit cost of Product 2 (P_y) Dollars

Total Budget (B) Dollars

Solving Utility Maximization Problem given Cobb-Douglas Utility Function

The goal: maximize total Utility

Max U(_x),_y) = A X_α y_β

Constraint: Total Budget B = P_xX + P_yY

Where:

P_x = Per unit cost of Product 1

P_y = Per unit cost of Product 2