5. A consumer lives on an island where she produces two goods, x and y, according...

 

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5. A consumer lives on an island where she produces two goods, x and y, according to the production possibility frontier x + y 200, and she consumes all the goods herself. Her utility function is U = xy. The consumer also faces an environmental constraint on her total output of both goods. The environmental constraint is given by x + y 20. (a) Write out the Kuhn-Tucker first-order conditions. (b) Find the consumer's optimal x and y. Identify which constraints are binding. 5. A consumer lives on an island where she produces two goods, x and y, according to the production possibility frontier x + y 200, and she consumes all the goods herself. Her utility function is U = xy. The consumer also faces an environmental constraint on her total output of both goods. The environmental constraint is given by x + y 20. (a) Write out the Kuhn-Tucker first-order conditions. (b) Find the consumer's optimal x and y. Identify which constraints are binding.