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Consider an optimization problem of maximizing utility u(x,y) = xy subject to the budget constraint 2x + y = 10 . Find the optimal consumption bundle , maximum utility and the value of the lagranfian multiplier. Interpret the multiplier in economic terms . If the income increase by 0.5 units , what is the change in the maximum utility , use multiplier to compute the result.
NOTE: the answer for the problem can be found by usual optimization method by changing the constraint to 2x + y = 10.5. But the idea behind it is to make use of lagrangian multiplier to solve such problems.
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