PPCs help to investigate the problems of growth and development also. In Figure 1.4, let FF be the production possibility curve for the year, say 2002 and let F’F’ be that for the year 2003. Since F’F’ is above FF at all levels of output of the two goods, it signifies growth of national product. Growth in this figure is uniform for both types of goods.
When growth is confined to the production of good X only, the PPC would blow out as in Figure 1.5, and when it is confined to the production of good Y, it would blow out as in Figure 1.6. If growth takes place in production of both the goods but is non-uniform, the PPC would blow out as in Figure 1.7.
Apart from the above, production possibility curves are put to another very important application—they play a significant role in resource allocation and re-allocation.
To elaborate, suppose an industry is currently producing quantities x and y of goods X and Y, respectively. Suppose further that product X fetches a price Px and product Y fetches a price Pv in the market so that the revenue, R, realised by the firm from the sale of quantities x and y of the two goods is given as
R =xPx+ yPy
The objective of the industry is to maximise revenue, R, subject to the limitations of the resources at its disposal. The limitation, known as constraint, restricts the industry to remain on its PPC. The problem of revenue maximisation, under the constraint of limited resources, can be stated as below.
Maximise, R = xPx+ yPv
Subject to, C = f(x, y)
Equation 1.3 represents the equation of the PPC. Condition of equilibrium can be shown to be tangency of the revenue line to the PPC, for which the slope of the PPC (dy/dx) must be equal to the slope of the revenue line (-Px/Py). In other words,
MRPTx,y = |-Px/Py|
In case product prices change, so would the slope of the revenue line as also the equilibrium of the industry. The following illustration would drive the concept home.
Quantities x and y of two goods X and Y, that are possible to be produced with given resource and technology being utilised fully and efficiently, are related through the following equation
12y = 36 – x2
Current prices of the two goods are Px = 12 and Pv = 24
(i) The maximum quantities of X and Y that are possible to be produced
(ii) Marginal Rate of Product Transformation, MRPTr y
(iii) Quantities of X and Y at the point of optimal resource allocation
(iv) Point of resource re-allocation when prices of the two goods change to
P1, = 15 and P = 18
(v) Revenue realised from the sale in (iii) and (iv) cases above.
(i) The maximum of y that is possible to be produced can be found by substituting x = 0 in the equation of the PPC. It is, thus, 3 units. Likewise maximum of x that is possible to be produced can be determined by substituting y = 0 in the equation of the PPC. It is x = 6.
For optimality of the resource allocation,
Slope of PPC = Slope of revenue line
= x/6 =1/2
= x = 3
Substituting, x = 3 in the equation of the PPC,
We have y = 2.25
Thus, the point of optimal resource allocation is (3, 2.25). Revenue at this point is
R = 3 ? 12 + 2.25 ? 24 = 36 + 54 = 90
(iv) Now product prices change to P1x = 15 and P1y = 18. The value of the slope of the revenue line changes to I -15/18 I = 5/6. The new revenue line,
R = 15x + 18y
would now touch the PPC at E1 instead of E0. For optimality,
Slope of PPC = Slope of Revenue line
= x/6 = 5/6
= x = 5
Corresponding value of y can be found by substituting x = 5 in the equation of the PPC. It works out to be 11/12 or 0.92. Revenue realised at this point is
R = 15 ? 5 + 0.92 ? 18 = 91.56
Point of resource allocation shifts from E0 to E1 this is known as resource re-allocation. The reader can interpret the movement from E0 to E1 as a consequence of rise in Px and fall in Py. Rise in Px would lead to production of higher quantity of X and fall in Py, to production of lower quantity of Y.
This explains how problems of allocation and re-allocation of resources are solved under competitive conditions that require equality of market price of a product to its marginal cost.
We have seen how a rise in market price of product X leads to an increase in its production, and how a fall in market price of product Y leads to a decrease in its production. Let us use these conclusions in classification of the existing production and consumption systems commonly known as ‘economic systems’.