Question

Potatoes cost Janice $1.00 per pound, and she has $5.00 that she could possibly spend on potatoes or other items. If she feels that the fist pound of potatoes is worth$1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all the subsequent pounds are worth $0.30, how many pounds of potatoes will she purchase?

Answer 1

1.5+1.14+1.05+(x-3)*0.3=5
x=7.36 pound

Answer 2

1.50 +1.14 + 1.05 + .30 + .30 + .30 +.30 = 4.89

The total she is willing to spend cannot surpass $5

She would buy 7 pounds.

Answer 3

She buys 3 pounds of potatoes.
Because upto 3rd pound the Marginal cost($1.00) of potato < Marginal Value($1.50, 1.14, 1.05).
From the 4th pound on the MV($0.30) < MC($1.00)

Answer 4

The store has gazillions of potatoes, which they value at $1.25/lb.
Janice has a lack of potatoes, and she values the first pound at $1.50. This discrepancy is what makes trade possible: a difference in valuation.

I believe that the writer has oversimplified the point this supposedly illustrates. If Janice is a completely rational consumer, she will buy only thefirst pound of potatoes at $1.50, regardless of how much larger her potato budget is. The second pound is worth only $1.14 to her, a loss of 11 cents ifshe buys it.

I believe that the book is trying to illustrate the principle of unit utility, which does not apply in this case. Unit utility (or whatever it's called inyour textbook) has us examining the unit price of Janice's choices as a whole:
weight . . value . . . unit-value
1 lb . . . . $1.50 . . . $1.50 / lb
2 lb . . . . $2.64 . . . $1.32 / lb
3 lb . . . . $3.79 . . . $1.26+ / lb
4 lb . . . . $4.09 . . . $1.02+ / lb

In this scenario, Janice would buy 3 pounds at $1.25/lb, since she believes the *average* value per pound is $1.263333... With only $3.00 to spend, shewould buy two pounds she could afford.

You see the principle? You see where the problem writer slipped up in the paradigm? As given, Janice still maximizes her overall valuation by stopping atone pound.

The correct paradigm for this is for the store manager to have a demand curve handy, and decide how large to make the sacks of potatoes the store will sellas its only packaging size. In this case, the store would package potatoes in 3-pound bags; all the Janices in town would deem the bag barely worth theprice, but buy them for the slim (four-cent) profits to their households.