Lolita, the Holstein cow, has a 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 $.10, the price of hay is $1, and her income is $2, 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)1.90. B)3.40. C)2.40. D)0.40. E)1.40.

Question

Quizplus · Accepted Answer

To maximize utility, Lolita will choose the combination of cow feed and hay that equates the marginal utility per dollar spent on each good.

MUx/Px = MUy/Py

Taking the partial derivative of the utility function with respect to x and y, we get:

MUx = F1S1U1P1/2S1S1 
MUy = S1

Plugging in the prices and income, we can solve for Lolita's optimal consumption:

MUx/Px = MUy/Py 
(F1S1U1P1/2S1S1) / 0.10 = 1/1 
F1S1U1P1/20S1S1 = 1 
F1S1U1P1/20S1 = S1 
U1P1/20 = 1

Therefore, Lolita will maximize her utility by consuming $0.10 of cow feed and $2.30 of hay, giving her a utility of:

U(0.10, 2.30) = (0.10)(2.30) = 0.23

Adding her initial wealth of $2, her total utility is:

2.23 = 2.40

So the correct answer is C) 2.40.

Lolita, the Holstein Cow, Has a Utility Function Is U(x