ª The algebraic formula for a production possibilities ...

Deriving an Algebraic Equation for the Production Possibilities Frontier

The algebraic formula for a production possibilities frontier (PPF) shows the

opportunity cost of one good in terms of the other.

The reciprocal of the opportunity cost shows the opposite¡ªthe opportunity cost of the

second good in terms of the first one.

Concave PPFs show increasing opportunity costs. Straight-line PPFs show constant

opportunity costs.

Bernie¡¯s PPF on the left tells us his

opportunity cost of scrubbing a room in

terms of how many rooms he cannot sweep.

You determine this by measuring the slope,

the rise divided by the run. In this case, the

slope throughout the PPF is ¨C2, meaning that

in order to scrub one room, he cannot sweep

two rooms.

Review: The slope is "rise/run." Using the

endpoints, it is 6/3 = ¨C2. The coefficient is

negative because of the inverse relationship.

By the reciprocal rule, you can reverse the

axes and determine the opportunity cost of

the other good. The intercepts of Bernie¡¯s

PPFs indicate the maximum amounts of

sweeping and scrubbing that he could do, as

shown on the vertical axes. The slope is the

opportunity cost of getting more of what¡¯s on

the horizontal axis in terms of what¡¯s on the

vertical. In the example on the left, Bernie's

opportunity cost of scrubbing a room is 2

swept rooms; his opportunity cost of sweeping

one room is 1/2 a scrubbed room.

Bernie¡¯s PPF is a straight line, meaning that his

resources are equally suited for either

sweeping or scrubbing. His opportunity costs

are constant. A PPF that is concave (far left

box) indicates increasing opportunity costs.

Increasing opportunity costs mean that not all

resources are equally suited for the production

of both goods.

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