International Trade Theory and Policy
by Steven M. Suranovic
The Ricardian Model PPF
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 LC and LW into the labor constraint yields the equation for the PPF.
This equation has three exogenous variables (aLC, aLW and L) which we assume have known values and two endogenous variables (QC and QW) 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 y-intercept. The PPF equation can be rewritten as,
We plot the PPF on a diagram with QC on the horizontal axis and QW on the vertical axis. The equation is easily plotted by following three steps.
Step 1) Set QC = 0 and solve for QW. In this case the solution is . This corresponds to the QW-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 Qw = 0 and solve for Qc. In this case the solution is, . This corresponds to the Qc-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 downward-sloping 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 - Chapter 40-3: Last Updated on 7/18/06