Question

R9. What is the relationship between the marginal products of the factors of production and the marginal rate of technical substitution?

(CANNOT READ THE HAND WRITTEN EXAMPLE so please don't just re-post that one.

Answer 1

Marginal rate of technical substitution is the rate at which a factor of production can be substituted for another factor in a way to produce a constant level of output.

Let the two commodities be X and Y and the two factors of production be Labor and Capital.

Thus, the MRTS between capital and labor is the rate at which labor can be substituted for capital in the production of Good X without changing the quantity of output.

Mathematically,

MRTS is the slope/gradient of the isoquant at a point.

Thus, MRTS = dK/dL = MP(l)/MP(k)

Since the isoquant is downwars sloping, its slope depicts the law of diminishing marginal productivities ( and hence is equivalent to MPL/MPK)

[Marginal productivity of a factor is defined as the change in productivity when one more unit of the factor is employed].