The production possibility frontier (PPF) is a graphical representation of the maximum possible combination of goods and services that an economy can produce given its resources and technology. It shows the trade-offs and opportunity costs faced by an economy when it allocates its resources to produce different goods and services.

A linear PPF implies constant opportunity cost. This means that the opportunity cost of producing one more unit of a good remains constant as more of that good is produced. Let's understand why this is the case:

1. Constant Opportunity Cost:
In a linear PPF, the slope of the curve is constant. The slope represents the opportunity cost of producing one good in terms of the other. If the slope is constant, it means that the opportunity cost of producing one more unit of a good remains the same, regardless of the initial production levels. This constant opportunity cost occurs when resources are easily adaptable between the production of different goods. For example, if an economy can easily switch resources between producing cars and producing computers without any additional costs, then the opportunity cost of producing one more car or one more computer will remain the same.

2. Economy is not stagnant:
A linear PPF does not imply that the economy is stagnant. It simply represents a specific trade-off between the production of two goods. The economy can still operate efficiently and produce at different points along the PPF, depending on its preferences and resource allocation.

3. No underemployment of factors of production:
Underemployment of factors of production refers to a situation where resources are not fully utilized. A linear PPF does not indicate underemployment of factors of production. It only shows the maximum possible output combinations given the available resources and technology. If the economy is operating on the PPF, it means that it is using all its resources efficiently.

4. Opportunity cost increases with production:
This statement is incorrect. In a linear PPF, the opportunity cost remains constant. It does not increase with production. The constant opportunity cost implies that the trade-off between producing one good and the other remains the same, regardless of the level of production.

In conclusion, if the production possibility frontier is linear, it implies constant opportunity cost. This means that the opportunity cost of producing one more unit of a good remains the same, indicating that resources are easily adaptable between the production of different goods.