how would the widespread use of a new type of chemical fertilizer affect a nation's production possibilities Frontier and why

A new fertilizer will shift the nations production possibilities upwards. This is because of the increasing productivity or returns from agriculture as the new fertilizer will enable farmers to increase their yield. The productions possibilities frontier will therefore increase to reflect the increased yield

The use of a new chemical fertilizer would move a nation's production possibility frontier outwards, as this measure is likely to result in higher outputs. This is because a new fertilizer is likely to provide nutrients to the soil that it previously lacked, benefitting the crops that are grown in that soil and increasing production.