Lolita, the Holstein cow, has a utility function is , 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

Lolita, the Holstein cow, has a utility function is  , 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.

Quizplus · Accepted Answer

Lolita's budget constraint can be written as 0.1x + y = 2, or y = 2 - 0.1x.
We can substitute this into her utility function to get:
U(x) = x(11 - 0.6x)
Taking the derivative with respect to x and setting it equal to zero to find the maximum: 
11 - 1.2x = 0
x = 9.1667
So, the optimal consumption is 9.1667 units of cow feed and y = 2 - 0.1(9.1667) = 1.0833 units of hay.
Plugging these values into the utility function:
U(9.1667, 1.0833) = 9.1667(11 - 0.6(9.1667)) + 1.0833(11 - 1.2(9.1667)) = 2.40
Thus, her utility will be 2.40 when she consumes 9.1667 units of cow feed and 1.0833 units of hay.

Lolita, the Holstein Cow, Has a Utility Function Is