Question

Potatoes cost Janice \(1 per pound, and she has \)5.00 that she could possibly spend on potatoes or other items. If she feels that the first pound of potatoes is worth \(1.50, the second pound is worth \)1.14, the third pound is worth \(1.05, and all subsequent pounds are worth \)0.30 per pound, how many pounds of potatoes will she purchase? How many pounds will she purchase if she has only $2 to spend?

Short answer

Janice will purchase three pounds of potatoes for $3.

If Janice has only $2 to spend, she will buy 2 pounds of potatoes.

Step-by-step solution

Step 1. Meaning of total and marginal utility

Total utility is the satisfaction received from all the units of the commodity consumed. It is the summation of all the marginal utilities.

TU_t = MU_t-1 + MU_t .

Here, MUt-1 and MUt are the marginal utilities of the previous unit and the marginal utility of the unit t, respectively.

Step 2. Pounds of potatoes that will be purchased by Janice

Janice witnesses the worth of potatoes (in dollars) per pound decline with each successive unit. The marginal and total utilities of potatoes on each pound are as follows.

Unit (in pound)	Marginal Utility (in dollars)	Total Utility (in dollars)
1	1.5	1.5
2	1.14	2.64
3	1.05	3.69
4	0.30	3.99

The marginal cost of each pound of potatoes is $1. The marginal benefit for each pound of potatoes is greater than the marginal cost till the third unit. After the third unit, the marginal utility for each unit is lower than the marginal cost. Therefore, she will accept only 3 pounds of potatoes.

Step 3. Deciding how many potatoes to buy with just $2

When Janice has only $2, the total benefit from two pounds of potatoes and the marginal benefit from the pounds of potatoes is more than her budget and the marginal cost. Thus, she will spend all the money on purchasing 2 pounds of potatoes.