Answer to Question #171471 in Microeconomics for Ishika

Question

show how a producer is in equilibrium when MTRS between 2 inputs is equal to their price ratio?

Answer 1

There are two essential or second order conditions for the equilibrium of the firm:

1. The first condition is that the slope of the iso-cost line must equal the slope of the isoquant curve. The slope of the iso-cost line is equal to the ratio of the price of labour (w) to the price of capital (r) i.e. w/r. The slope of the isoquant curve is equal to the marginal rate of technical substitution of labour and capital (MRTSLC) which is, in turn, equal to the ratio of the marginal product of labour to the marginal product of capital (MPL/MPC).

Thus the equilibrium condition for optimality can be written as:

W/r = MPL/MPC = MRTSLC

2. The second condition is that at the point of tangency, the isoquant curve must he convex to the origin. In other words, the marginal rate of technical substitution of labour for capital (MRTSLC) must be diminishing at the point of tangency for equilibrium to be stable.