In: Math
If x 1 and x 2 are the number of items of two goods bought, a customer’s utility is U ( x 1 , x 2 ) = 2 x 1 x 2 + 3 x 1 . The unit cost is $ 1 for the first good and $ 3 for the second. Use Lagrange multipliers to find the maximum value of U if the consumer’s disposable income is $ 100 . Estimate the change in optimal utility if the consumer's disposable income increases by $ 8 .