Refer to the following graph:
The price of X is $20 and the price of Y is $40.

-How many units of X will the consumer choose if point B is the utility-maximizing choice?
A) 28
B) 30
C) 32
D) 60
E) none of the above

Question

Refer to the following graph:
The price of X is $20 and the price of Y is $40.
 
-How many units of X will the consumer choose if point B is the utility-maximizing choice?
A) 28 
B) 30 
C) 32 
D) 60 
E) none of the above

Quizplus · Accepted Answer

At point B, the consumer is willing to give up 2 units of Y to gain 1 unit of X. This means the marginal rate of substitution (MRS) is 2. At $20 for X and $40 for Y, the consumer can afford to buy (5/4) units of Y for every unit of X. This means the slope of the budget constraint is -(5/4). Equating the MRS with the slope of the budget constraint, we get 2=-(5/4), which gives us X=32. Therefore, the consumer will choose 32 units of X when point B is the utility-maximizing choice.

Refer to the Following Graph