Suppose that $U ( x , y ) = \min ( 3 x , y )$. Further suppose that $P _ { x } = \$ 5$ per unit and $P _ { y } = \$ 10$ per unit and income is $I = \$ 105$. For this consumer, the optimal basket to buy would be which of the following?
A) $( x , y ) = ( 9,3 )$
B) $( x , y ) = ( 3,1 )$
C) $( x , y ) = ( 1,3 )$
D) $( x , y ) = ( 3,9 )$

Question

Quizplus · Accepted Answer

The utility function $U(x, y) = \min(3x, y)$ suggests perfect complements, meaning the consumer wants to maintain the ratio $3x = y$. Given the budget constraint $5x + 10y = 105$, solving for $x$ and $y$ under the condition $3x = y$ gives the optimal basket $(x, y) = (3, 9)$.

Suppose That U(x,y)=min⁡(3x,y)U ( x , y ) = \min ( 3 x , y )U(x,y)=min(3x,y)

Suppose That $U ( x , y ) = \min ( 3 x , y )$