Opportunity Cost - The Slope of the PPF

The green segment shown in the PPF is tangent to the curve at the point selected. The slope of this segment approximates the slope of the PPF at the point of tangency. The segment has a length and is equal to 20 units.
The point selected is shown as point A. The level of food is 39 and the corresponding production of cloth is 69.8 . Suppose there is a decision to increase the production of food from point A. This would imply moving along the PPF to increase food production and would involve reducing cloth production if the economy is to stay on the PPF and remain efficient. That is, by reducing cloth production, the resources could be freed to produce more food.

The slope of the PPF is equal to C / F and the slope of the PPF is defined as the opportunity cost price of food (OC PF). In the lower graph in the diagram, the slope of the PPF (as measured by the slope of green tangent segment) calculated at each level of food production. The absolute value of the slope appears on the graph.

At point A, the slope of the PPF when food is 39 is equal to 0.55 (C/F). This measure of slope is opportunity cost of food production meaning that in order to produce one more unit of food, 0.55 units of cloth must be sacrificed.

The slope of segment is calculated as the change in cloth divided by the change in food along the length of the segment C /F. The shaded rectangle around the green segment in the PPF graph appears in a separate graph below (entitled Graph 2 - PPF Detail). In Graph 2, the shaded area of the PPF is expanded to analyse the slope of the segment.

For point A, selected on the PPF, the slope of the tangent segment (in green) approximates the actual slope of the PPF at that point. Notice that the slope of the PPF is negative and, the absolute value of the slope is shown on the graph. Along the green tangent segment, that just touches the PPF at point A, the upper end of the segment is the point C0=74.7 and F0=30.2. The bottom end of the segment is the point C1=64.9 (C) and F1=47.7 (F). Thus:
C = C1 - C0 = 64.9 - 74.7 = -9.75 (C)
F = F1 - F0 = 47.7 - 30.2 = 17.46 (F)
and the slope of the green tangent segment is:
C / F = -9.75 / 17.46 = -0.558 (C/F)

Now suppose there is a one unit increase in the quantity of food, starting at point A, moving to to point B. Re-allocating resources will divert some resources needed for the production of cloth at point A and will reduce cloth production but, the resources freed from cloth production become the inputs to increase food production by one unit. At point B, food production has increased to 40 and cloth output has been reduced from 69.849 to 69.282 (an additional two digits of decimal precision has been added to the original cloth production).

The slope of the PPF may also be calculated using the change in cloth for this one unit change in food output. Using a one unit change in food, and the change in cloth equal to: C = 69.282 - 69.849 = -0.567. Then the slope based on the one unit increase in food production is: C/ F = -0.567/1 = -0.567. This may be compared to the exact value of the slope (-0.558) calculated using the green segment. The difference is small and the student may prefer to use a one unit change in food production as the basis of calculating the slope.

As previously explained, the slope of the PPF is defined as the opportunity cost of a unit of food (the variable on the horizontal axis). It is also can be considered as a simple way to describe the supply curve. The 'OC' price of food, shown on the vertical axis in the lower diagram, increases as more is produced. In micro economics theory, the law of supply is derived from production and cost theory showing the supply curve is upward sloping. The PPF explains increasing opportunity costs of production are due to the scarcity of resources on the island and the imperfect substitution of resources.




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page updated 3 Dec 03