Final answer:
The Inada conditions are assumptions in economic models that ensure the existence of a unique steady state capital stock and are directly related to the diminishing marginal product of capital. They do not lead to divergence, constant levels, nor explosive growth in capital stock. Instead, they help model the convergence to a steady state where savings and investment are balanced.
Step-by-step explanation:
The Inada conditions pertain to the production function in economic models, which are constraints ensuring the existence of a unique steady state capital stock. Specifically, these conditions assume that capital has a diminishing marginal product, meaning that as more capital is added to production, the additional output produced from each new unit of capital decreases. This is seen as a movement along the production function curve.
In the context of a standard production function like the Cobb-Douglas, the Inada conditions imply that as the amount of capital grows infinitely large, the marginal product of capital approaches zero. Conversely, as the capital stock approaches zero, the marginal product of capital goes to infinity. These conditions ensure that the economy will reach a steady state where savings equal investments, as dictated by the national saving and investment identity which must always hold.
With respect to the options provided:
- a) Inada conditions ensure divergence in capital stock - Incorrect, because they ensure convergence to a steady state.
- b) Inada conditions ensure a constant capital stock - Incorrect, because the steady state refers to the situation where the capital stock does not need to change since savings and investments are in equilibrium.
- c) Inada conditions guarantee explosive growth in capital stock - Incorrect, as they do not imply unbounded growth but rather convergence to a steady state.
- d) Inada conditions are irrelevant to steady state capital stock - Incorrect, as they are critical to the determination of the steady state capital stock.