Question

Solve Lagrange function to maximize the utility function ( f(x, y) = x y² ) if $60 is available and the cost of a unit of x is $1 and the cost of a unit of y

Answer 1

To maximize the utility function f(x, y) = x y² using the Lagrange function, set up the Lagrange function with the constraint equation and available income. Find the critical points by taking the partial derivatives and setting them equal to zero. Solve the resulting equations to get the optimal values of x and y.

Step-by-step explanation:

Solving the Lagrange Function to Maximize Utility

To solve the Lagrange function for maximizing the utility function f(x, y) = x * y², we need to set up the Lagrange function and find the critical points. The Lagrange function is:

F(x, y, λ) = f(x, y) - λ * (c - I)

where c is the constraint equation and I is the available income. In this case, the constraint equation is c = x + y.

By taking the partial derivatives and setting them equal to zero, we can find the critical points. Solving these equations will give us the optimal values of x and y that maximize the utility function.