Question

(a) Does the assumption of diminishing marginal product of an inputs x1 and x2 imply strictly convex isoquant curves?

(b)Does the assumption of strictly convexity in the isoquant curves imply diminishing marginal products to input factors x1 and x2.

Answer 1

(a) The assumption of diminishing marginal product of an inputs x1 and x2 may imply strictly convex isoquant curves.

The marginal rate of technical substitution between inputs x1 and x2 is defined as the quantity of x2 which can be given up in exchange for an additional unit of x1. It can also be defined as the slope of an isoquant.

MRTSx1x2 = – ∆x2/∆x1 = dx2/ dx1 .............................. (1)

Where ∆x2 is the change in x2 and ∆x1 is the change in x1.

Due to falling MRTS, the isoquant is always convex to the origin.

(b) The assumption of strict convexity in the isoquant curves implies diminishing marginal products to input factors x1 and x2.convexity of an isoquant implies that the MRTS diminishes along the isoquant.

Equation (1) states that for an increase in the use of x1, fewer units of x2 will be used. In other words, a declining MRTS refers to the falling marginal product of x1 in relation to x2. To put it differently, as more units of x1 are used, and as certain units of x2 are given up, the marginal productivity of x1 in relation to x2 will decline.