To determine the opportunity cost for the United States to produce corn, we need to consider what must be given up in terms of diamonds to produce additional units of corn.
The opportunity cost is defined as the value of the next best alternative that is foregone when a particular decision is made. In this case, the U.S. must give up producing diamonds to produce corn.
Here's a step-by-step solution to find the opportunity cost:
1. Identify the production quantities:
- The United States can produce 60 units of corn or 10 units of diamonds in one week.
2. Calculate the opportunity cost of producing corn in terms of diamonds:
- To determine how many diamonds are given up per unit of corn, use the ratio of the total number of diamonds to the total number of corn. This is calculated as:
[tex]\[
\text{Opportunity cost of corn} = \frac{\text{Diamonds given up}}{\text{Corn produced}} = \frac{10}{60}
\][/tex]
3. Simplify the fraction:
- Simplifying [tex]\(\frac{10}{60}\)[/tex]:
[tex]\[
\frac{10}{60} = \frac{1}{6}
\][/tex]
Thus, the opportunity cost for the United States to produce corn is [tex]\(\frac{1}{6}\)[/tex] diamonds per unit of corn.
Given the provided answer choices, none of them explicitly shows [tex]\(\frac{1}{6}\)[/tex]. However, [tex]\(\frac{60}{10}\)[/tex] is a common mistake where the fractions are reversed.
The correct fraction representing the opportunity cost for the United States to produce corn is:
[tex]\[
\frac{10}{60} = \frac{1}{6}.
\][/tex]
For the problem's context, it should be noted:
- [tex]$60 / 10$[/tex] simplifies to 6, which is incorrect.
- [tex]$1 \%$[/tex] (1 percent) does not represent the opportunity cost here.
- [tex]$20 / 5$[/tex] results in 4 and is the relative opportunity cost for Congo, not the United States.
- [tex]$5 / 20$[/tex] simplifies to 0.25, which is unrelated to the U.S. data.
Therefore, the fraction [tex]\(\frac{10}{60}\)[/tex] or [tex]\(\frac{1}{6}\)[/tex] accurately represents the opportunity cost for the United States to produce corn.
