**In this article we will discuss about the meaning of a production possibility curve. **

Suppose a farmer has one input with which he can produce two products namely Y_{1} and Y_{2}. We assume that the other inputs are highly specialized and can be used for producing a specific crop only. So, problem of their allocation over various crops does not arise. With the given input x_{1} the farmer can produce either only Y_{1} or only Y_{2} or some combination of these two crops.

**How much of Y _{1} or Y_{2} can be produced with x_{1} depends upon the production functions given below: **

If is evident from the above that if the farmer has only 6 units of x_{1} he can either produce 24 units of Y_{1 }or 39 units of Y_{2}.

ADVERTISEMENTS:

If instead of producing only Y_{1 }or only Y_{2} , the farmer chooses to produce both Y_{1} & Y_{2} with x_{1} he can have many combinations of these crops.

Below we give some of these combinations of Y_{1} & Y_{2} based upon the above production functions, on the assumption that (a) he has only 4 units of x_{1} (input) and (b) he has only 6 units of x_{1}.

Various combinations of Y_{1} and Y_{2} in the above schedule represent production possibilities with four units and six units of the variable input x_{1 }Production possibilities, we may state, show all possible combinations of two or more products that can be obtained using the same amount of variable input say, x_{1}. The graphic representation of these production possibilities (in case of two commodities) is named as a production possibility curve, or a production possibility frontier which is depicted in Fig. 21.

In Fig. 21 whereas production possibility curve AA’ shows all combinations of two products Y_{1} and Y_{2} that can be produced by using four units of variable input x_{1} production possibility curve BB’ shows combinations of Y_{1 }& Y_{2} which can be produced with six units of variable input x_{1.}

These curves are also known as product transformation curves because one product is transformed into another product, (not physically) by transferring from one product to another. Finally these may also be called iso-resource curves because each output combination on any of such curves uses the same amount of resources.

**The Marginal Rate of Product Substitution (MTPS) or Marginal Rate of Transformation:**

ADVERTISEMENTS:

MRPS measures the extent to which the quantity of one product changes when the output of the other product is increased by one unit, provided that the total amount of the input used to produce them remains constant.

**The marginal rate of product substitution of Y _{2} for Y_{1} given by: **

In other words, if we are given a production possibility curve, MRPS is represented by the value of the slope of the production possibility curve at a given point. The slope of production possibility curve is generally negative.