Lolita's utility function is U(x, y)  x  x²/2  y, where x is her consumption of cow feed and y is her consumption of hay.If the price of cow feed is $.60, the price of hay is $1, and her income is $4 and if Lolita chooses the combination of hay and cow feed that she likes best from among those combinations she can afford, her utility will be

A) 4.08.
B) 3.40.
C) 0.08.
D) 6.08.
E) 2.08.

Question

Jocelyne Magdaleno · Accepted Answer

Final Answer : A, Explanation :  We need to find the combination of cow feed and hay that maximizes Lolita's utility given her budget constraint.Her budget constraint is: 0.6x + y = 4Solving for y, we get: y = 4 - 0.6xSubstituting y in her utility function, we get:U(x) = x(4 - 0.6x) - 0.5x^2To maximize this function, we take the derivative with respect to x and set it equal to 0:U'(x) = 4 - 1.2x - x = 0Solving for x, we get: x = 2Substituting x in the budget constraint, we get: y = 1.2So the combination of cow feed and hay that maximizes Lolita's utility is x = 2 and y = 1.2.Substituting these values in her utility function, we get:U(2, 1.2) = 2(4 - 0.6(2)) - 0.5(2)^2 + 1.2U(2, 1.2) = 4.08Therefore, Lolita's utility will be 4.08 when she consumes 2 units of cow feed and 1.2 units of hay.

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