Slope of isoquant curve/Marginal rate of substitution

The isoquant curve is convex to origin because of the law of diminishing marginal productivity

Marginal rate of substitution –
In Indifference curve analysis, Marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of satisfaction.
And for isoquants, Marginal rate of substitution can be defined as the the rate at which one factor must be added to compensate for the loss of another factor, to keep output constant
Marginal rate of substitution is the slope of the isoquant curve.
The absolute value of the slope at a point on the isoquant curve equals the ratio of the marginal productivity of labor to the marginal productivity of Capital.


Slope = MPlabour / MPcapital = Marginal rate of substitution


MP labour = Marginal Productivity of labour
MP capital = Marginal Productivity of capital

Marginal Productivity of a factor can be defined as the change in productivity as one more unit of facor is employed.