Why does the marginal rate of technical substitution (MRTS) decline as we move rightward and downward along a convex-shaped isoquant?

Declining Marginal Rate of Technical Substitution (MRTS) Along a Convex Isoquant

The Marginal Rate of Technical Substitution (MRTS) is the rate at which one input can be substituted for another while keeping the output constant. In the context of a convex-shaped isoquant, the MRTS declines as we move rightward and downward along the curve.

1. Diminishing Marginal Productivity: The fundamental reason for the declining MRTS is the law of diminishing marginal productivity. As more of one input (say, labor) is used while reducing the other input (say, capital), the additional output produced by each additional unit of labor begins to decrease.

2. Substitutability of Inputs: Initially, when a large amount of capital and a small amount of labor are used, a small reduction in capital can be compensated with a small increase in labor with little loss in productivity. However, as we continue to substitute labor for capital, each additional unit of labor becomes less effective because the proportion of capital to labor becomes increasingly smaller.

3. Convex Shape of Isoquant: The convex shape of the isoquant reflects the decreasing substitutability of inputs. It indicates that as the proportion of one input increases, it becomes increasingly difficult to replace the other input without losing productivity.

In summary, the declining MRTS along a convex-shaped isoquant is a result of the diminishing marginal productivity of inputs and the decreasing ease of substitutability between these inputs as their relative proportions change.