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# Maximise utility with the Lagrange method in this case.

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Let U(x,y)= Ax^ay^b be the utility function of an individual. The individual has x hour leisure time per day and consumers y units of other goods. The individual works and is paid w \$ per hour. The average price of the other goods is p \$. We assume that the individual spends his/her total income i.e.

py = w(24 - x)

Use the Lagrange method to determine how many hours this individual works per day to maximize the utility.

https://brainmass.com/economics/utility/maximize-utility-lagrange-method-427268

#### Solution Preview

To use the Lagrange Multiplier, we first set up the Lagrange equation.

&#923; = f(x,y) + &#955;[g(x,y) - c]. where f(x,y) is the function we want to maximize (or minimize), and g(x,y) = c is the constraint. &#955; is a free parameter.

In our case, the function f(x,y) = A(x^a)(y^b), and the constraint is py = 24w - wx, or wx + py = 24w

&#923; = A(x^a)(y^b) + ...

#### Solution Summary

This solution explains how to maximize utility with the Lagrange method.

\$2.19