To determine the opportunity cost for the United States to produce corn, we must consider the alternative goods that must be foregone to produce an additional unit of corn.
From the given data:
- The United States can produce 60 units of corn or 10 units of diamonds in one week.
### Calculating the Opportunity Cost for Corn in the United States
The opportunity cost of producing corn in terms of diamonds can be calculated by dividing the amount of diamonds foregone by the amount of corn produced.
Here are the steps in detail:
1. Identify Production Possibilities:
- The United States has the capacity to produce either 60 units of corn or 10 units of diamonds in one week.
2. Determine the Opportunity Cost:
- Opportunity cost of producing 1 unit of corn = (Units of diamonds foregone) / (Units of corn produced)
- Calculate: [tex]\( \frac{10 \text{ units of diamonds}}{60 \text{ units of corn}} = \frac{1}{6} \text{ units of diamonds per unit of corn} \)[/tex]
3. Convert to Fractional Form:
- To match it with one of the provided choices, we take the reciprocal for clear representation:
[tex]\[
\frac{corn}{diamonds} = \frac{60 \text{ units of corn}}{10 \text{ units of diamonds}} = 6
\][/tex]
### Matching the Opportunity Cost with the Given Choices
The options provided are:
- [tex]\( 60/10 \)[/tex]
- [tex]\( 10/80 \)[/tex]
- [tex]\( 20/5 \)[/tex]
- [tex]\( 5/20 \)[/tex]
Out of these choices, the fraction [tex]\( \frac{60}{10} \)[/tex] is consistent with our opportunity cost representation, i.e., 6.
Thus, the fraction that represents the opportunity cost for the United States to produce corn is:
[tex]\[ \boxed{60 / 10} \][/tex]
