Question

Spud really likes potatoes. At best any other goods are worth less than $0.50 to him, potatoes cost $0.75 per pound, and he has $4.00 that he could possibly spend on potatoes or other items. Suppose he feels that the first pound of potatoes is worth $1.00, the second pound is worth $0.90, the third pound is worth $0.70, and all subsequent pounds are worth $0.25. Calculate how many pounds of potatoes Spud will purchase and explain why he will purchase this amount.

Answer 1

Spud will purchase 5 pounds of potatoes because the total value he assigns to them is less than the total amount he can spend.

Step-by-step explanation:

To calculate how many pounds of potatoes Spud will purchase, we need to determine the maximum amount he can spend on potatoes. Given that Spud has $4.00 and potatoes cost $0.75 per pound, we can divide the total amount available by the cost per pound: $4.00 ÷ $0.75 = 5.33 pounds (rounded down to 5 pounds).

Now, let's calculate the total value Spud assigns to each pound of potatoes. For the first pound, he values it at $1.00. For the second pound, he values it at $0.90. For the third pound, he values it at $0.70. And for all subsequent pounds, he values them at $0.25. To determine the total value Spud assigns to 5 pounds of potatoes:

1. First pound: $1.00
2. Second pound: $0.90
3. Third pound: $0.70
4. Fourth pound: $0.25
5. Fifth pound: $0.25

Total value: $1.00 + $0.90 + $0.70 + $0.25 + $0.25 = $3.10

Since the total value assigned to the potatoes ($3.10) is less than the total amount Spud can spend ($4.00), he will purchase the maximum amount of 5 pounds of potatoes.