A typical, bowed-out production possibility frontier between two goods—guns and butter—shows that the opportunity cost of butter in terms of guns increases as more butter is produced. This implies that the opportunity cost of guns in terms of butter decreases as more guns are produced. True or false?

The opportunity cost is the cost that an economy faces when people decide to do something and not doing another thing. In this case, the opportunity cost of producing butter is not producing guns and in the same way, the opportunity cost of producing guns is to not produce butter. Then, if the economy produces more butter, the opportunity cost in terms of guns increases because resources are being used in butter and not in guns.

For example:

I have 20 units of resources and to produce 1 gun or 1 butter I spend 1 unit of those resources. If I was producing 15 butters and 5 guns and then I increase butter production to 18, the opportunity cost in terms of guns is that I am producing 3 guns less, my cost is 3 guns less. If I decide to increase the butter production to 19 units, my cost is 4 guns less.

In the same way, if the economy produces more guns, the opportunity cost in terms of butter increases because resources are being used in guns and not butter. Thus, it is false that as more guns are produced, the opportunity cost of guns in terms of butter decreases. As more guns are produced, the economy is sacrificing more units of butter, then the opportunity cost, in terms of butter, increases.