Using the two production functions and the labor constraint we can
describe the production
possibility frontier (or PPF). First, note that the production functions can be rewritten as and
. Plugging
these values for L_{C} and L_{W} into the labor constraint yields the
equation for
the PPF.
This equation has three exogenous variables (a_{LC}, a_{LW} and L)
which we assume have known values
and two endogenous variables (Q_{C} and Q_{W}) whose values must be
solved for. The PPF equation is
a linear equation, i.e it describes a line. With some algebraic manipulation we can rewrite the PPF
equation into the standard form for an equation of a line, generally written as (y = mx + b), where
y
is the variable on the vertical axis, x the variable on the horizontal axis, m is the slope of the line
and
b is the yintercept. The PPF equation can be rewritten as,
We plot the PPF on a diagram with Q_{C} on the horizontal axis and
Q_{W} on the vertical axis. The
equation is easily plotted by following three steps.
Step 1) Set Q_{C} = 0 and solve for Q_{W}. In this case the
solution is . This
corresponds to the Q_{W}intercept. It tells us the quantity of wine that the US could
produce if it devoted all of its labor force (L) to the
production of wine.
Step 2) Set Q_{w} = 0 and solve for Q_{c}. In this
case the
solution is, . This
corresponds to the Q_{c}intercept. It
tells
us the quantity of cheese that the US could
produce if it devoted all of its labor force (L) to the
production of cheese.
Step 3) Connect the two points with a straight line.
The straight downwardsloping line is the production possibility frontier. It describes all
possible
quantity combinations of wine and cheese that can be achieved by the US economy. A
movement
along the curve represents a transfer of labor resources out of one industry and into another such
that
all labor remains employed.
Points inside the PPF are production possibilities but correspond to underemployment
of labor resources. In fact all production possibilities regardless of
whether full employment is fulfilled is referred to as the production
possibility set (PPS). The PPS is represented by all of the points within
and on the border of the red triangle in the diagram.
International Trade Theory and Policy Lecture Notes:
©19972006 Steven M. Suranovic
Last Updated on 7/18/06
