 If good 1 is an investment good governed by the equation
and good 2 be a consumption good governed by the equation
then rental and wage rates can be calculated by optimizing a representative firm's profit function, giving
for the rental rate of capital, "r", and
for the wage rate of labor, "w", so the input price ratio, formula_5, is
Normalizing this equation by letting formula_8, and solving for formula_9 provides the formulas to be graphed in the first quadrant.On the other hand, normalizing the equation
and solving for the price ratio, formula_12 provides the formula which is to be graphed in the fourth quadrant.Graphing these three functions together shows the relationship.