Use the following to answer question:
-(Table: Marginal Utility per Dollar IV)Use Table: Marginal Utility per Dollar IV.If Ashyra has $40 to spend on potatoes and clams,then the utility-maximizing combination is _____ pound(s)of clams and _____ pound(s)of potatoes.
A)3;4
B)2;5
C)1;8
D)2;6

Question

Use the following to answer question: 
-(Table: Marginal Utility per Dollar IV)Use Table: Marginal Utility per Dollar IV.If Ashyra has $40 to spend on potatoes and clams,then the utility-maximizing combination is _____ pound(s)of clams and _____ pound(s)of potatoes. 
A)3;4 
B)2;5 
C)1;8 
D)2;6

Quizplus · Accepted Answer

To find the utility-maximizing combination, we need to compare the marginal utility per dollar of potatoes and clams. From the table, we can see that the marginal utility per dollar of the last pound of potatoes is 12 and the marginal utility per dollar of the last pound of clams is 8. Therefore, Ashyra should purchase more potatoes and fewer clams.

Let x be the number of pounds of clams and y be the number of pounds of potatoes.

We know that the price of clams is $5 per pound, and the price of potatoes is $3 per pound. Ashyra's budget is $40, so we have:

5x + 3y = 40

Solving for x in terms of y, we get:

x = (40 - 3y) / 5

Now we can calculate the marginal utility per dollar of each option.

For clams:

MU per dollar = MU / Price = 8 / 5 = 1.6

For potatoes:

MU per dollar = MU / Price = 12 / 3 = 4

We want to maximize the total marginal utility per dollar, so we need to choose the option with the highest MU per dollar ratio.

Substituting the expression for x into the formula for MU per dollar for clams, we get:

MU per dollar for clams = MU / Price = (24 - 4y) / 5

Setting this equal to the MU per dollar for potatoes, we get:

(24 - 4y) / 5 = 12 / 3

Simplifying, we get:

24 - 4y = 20

4y = 4

y = 1

So Ashyra should buy 1 pound of potatoes and:

x = (40 - 3y) / 5 = 7

Therefore, the utility-maximizing combination is 1 pound of potatoes and 7 pounds of clams.

The correct answer is D.

Use the Following to Answer Question