Consider the following combinations of guns and butter that can be produced 0 guns, 20,000 units of butter, 5,000 guns, 15,000 units of butter, 10,000 guns, 10,000 units of butter, 15,000 guns, 5,000 units of butter 20,000 guns, 0 units of butter. The PPF between guns and butter is a a downward-sloping bowed-out curve b a downward-sloping straight line c an upward-sloping straight line d it is impossible to answer this question without knowing which good would be plotted on the vertical axis

Production Possibility Frontier is downward sloping because of negative relationship between two goods , one good can be increased by reducing other - given same resources & technology.

The slope of PPF depends on Marginal Opportunity Cost i.e amount of a good sacrifised to gain an additional of the other one i.e Δgood sacrifised / Δgood gained . If MOC is constant : PPF is a straight line (like in this case) ; If MOC is increasing (general case - due to resource shift from efficient to inefficient good production) : PPF is concave / outward bowed curve ; If MOC is decreasing : PPF is convex .

As per given schedule :

Guns Butter MOC (Δgood sacrifised / Δgood gained)

0 20000 _

5000 15000 5000 / 5000 = 1

10000 10000 5000 / 5000 = 1

15000 5000 5000 / 5000 = 1

2000 0 5000 / 5000 = 1

As it can be seen : Guns are increasing & Butter are falling , so these have inverse relationship & PPF is downward sloping .The ratio of butter sacrifised to gain guns is constant, so MOC is constant & PPF is straight line.