Question

(a) What is the efficient production set? Explain using a diagram

Answer 1

A production set refers to all possible combinations of inputs and outputs that can be achieved through production, with a given level of technology. Production is said to be efficient when the factor endowments for producing goods have been efficiently allocated. A production possibility frontier (PPF) shows all maximum possible outputs for two goods, when a set of inputs and resources is given and technology is assumed to be constant. In theory of production, an isoquant is defined as the locus of combinations of two inputs at a given level of technology, for which the level of output remains constant.

Let us assume that two goods are produced in the economy (goods A and B), with two factors of production (labour ‘L’ and capital ‘K’). It is when the two isoquants for good A and B are tangent to each other, is the production called efficient. Similar to cases in General Equilibrium theory, a Production Edgeworth Box can be used to explain the concept of efficient production sets better. From the efficient allocations inside a Production Edgeworth Box, a PPF is derived using the information of efficient allocation to maximize the benefits available to consumers out of the two goods A and B. However, the Production Edgeworth Box is central to the concept of an efficient production set for analyzing efficiency in production. This is done below in a 2X2 (2 goods, 2 factors of production) framework.

Let both A and B’s production functions be dependent on Labour and Capital where A=A(La, Ka) and B=B(Lb,Kb). The total labour and capital endowments in the economy are: L=La+Lb and K=Ka+Kb. It is assumed that all resources have been used and there is no unemployment. In diagram 1 of the Production Edgeworth Box, lower left corner depicts 0 output of good A and upper right corner depicts 0 output of good B. As one moves along isoquants from lower left to upper right corner, there is an increase in output of good A and a decrease in output of B. This is because, since resources (L and K) are limited in the economy, increase in production of A shifts resources from B to A and thereby reduces available resources for the production of B. Thus an increase in A leads to a fall in B and vice versa.

In diagram 1, a series of isoquants in pink represent production of A and those in blue represent production of B. Whenever the isqouants are tangent to each other, the marginal rates of technical substitution of both the goods are equal. At that point, it is not possible to increase the production of one good without reducing the production of the other good. If we move from the point of tangency (t) to a point s, then the production of A increases but that of B falls. Similarly if we move from t to r, the production of B rises but that of A falls. Now let point 't' of production require La units of labour and Ka units of capital. Therefore, Lb= L-La and Kb=K-Ka (from labour and capital endowment equations). Thus the production of good B will now be B=B(L-La,K-Ka) and that of A will be A=A(La, Ka). This represents an efficient production point. In a Production Edgeworth Box, there can be more than one such point of tangency representing multiple efficient production points. A set containing these efficient production points is said to be an efficient production set.

The curve joining all the points of efficient production is called the Contract curve. A PPF corresponding to this Contract curve is drawn in diagram 2, which finally shows the efficient production set. Thus, diagram A first locates all the efficient points of production along with other inefficient points of production. Diagram B singles out the efficient production points, makes a Contract curve join those points and derives a PPF corresponding to that contract curve to derive the efficient production set.