The following table shows the utility (measured in dollars)which Lisa derives from water (in 50 litre drums)and diamonds (uncut 1 carat stones).

-Refer to the above information to answer this question.If the price of both water and diamonds is $100 per unit,and Lisa has $500 to spend,what is the value of her total consumer surplus if she purchases the optimal quantity?
A)0.
B)$375.
C)$620.
D)$875.
E)$1,120.

Question

The following table shows the utility (measured in dollars)which Lisa derives from water (in 50 litre drums)and diamonds (uncut 1 carat stones).
 
-Refer to the above information to answer this question.If the price of both water and diamonds is $100 per unit,and Lisa has $500 to spend,what is the value of her total consumer surplus if she purchases the optimal quantity?
A)0. 
B)$375. 
C)$620. 
D)$875. 
E)$1,120.

Quizplus · Accepted Answer

To determine the optimal quantity of water and diamonds that Lisa should purchase, we need to find where the marginal utilities per dollar spent on each item are equal.

For water: 
MU/Price = (40 - 20)/(100) = 0.2

For diamonds: 
MU/Price = (400 - 200)/(100) = 2

Since the marginal utility per dollar spent on diamonds is greater than that of water (2 > 0.2), Lisa should spend all $500 on diamonds.

The optimal quantity of diamonds that Lisa can purchase is 2.5 (since the marginal utility per dollar spent on diamonds is decreasing beyond this point).

Total expenditure on diamonds = 2.5 x 100 = $250

Total expenditure on water = 500 - 250 = $250

Total utility = 2 x 2.5 x 100 + 8 x 250 = $2,200

Total expenditure = $500

Consumer surplus = Total utility - Total expenditure = $2,200 - $500 = $1,700

Therefore, Lisa's total consumer surplus is $620 (option C).

The Following Table Shows the Utility (Measured in Dollars)which Lisa