To determine the opportunity cost for the United States to produce corn, we'll analyze the data given in the table:
[tex]\[
\begin{array}{|c|c|c|}
\hline
& \text{Corn} & \text{Diamonds} \\
\hline
\text{United States} & 60 & 10 \\
\hline
\text{Congo} & 20 & 5 \\
\hline
\end{array}
\][/tex]
We'll focus on the production capabilities of the United States. The United States can produce 60 units of corn and 10 units of diamonds in one week. The opportunity cost of producing one unit of corn for the United States is how many units of diamonds it has to give up to produce one more unit of corn.
First, we need to find out how many units of diamonds are foregone when the United States produces one more unit of corn. This can be done by calculating the ratio of diamonds to corn. The formula for calculating the opportunity cost of producing one unit of corn is:
[tex]\[
\text{Opportunity cost of 1 unit of corn} = \frac{\text{Units of diamonds foregone}}{\text{Units of corn produced}}
\][/tex]
Plugging in the given values:
[tex]\[
\frac{\text{United States Diamonds (10)}}{\text{United States Corn (60)}} = \frac{10}{60}
\][/tex]
Simplify this fraction:
[tex]\[
\frac{10}{60} = \frac{1}{6}
\][/tex]
Therefore, the opportunity cost for the United States to produce one unit of corn is [tex]\( \frac{1}{6} \)[/tex] of a unit of diamonds. In decimal form, this equates to approximately 0.167.
Given the provided options, the correct fraction representing the opportunity cost for the United States to produce corn is [tex]\(\frac{10 \% 6}{6}\)[/tex], as it simplifies to [tex]\(\frac{1}{6}\)[/tex].
