Final answer:
In the Solow growth model, Country B with the lower initial capital per worker (k) will have a higher initial marginal product of capital (MPK) and a higher growth rate for k when both countries are below their steady state levels and have the same savings rates and technology.
Step-by-step explanation:
The Solow growth model is a framework used to analyze the dynamics of economic growth and capital accumulation. In the given production function Y = F(K, N) = K0.3 N0.7, the marginal product of capital (MPK) is the increase in output (Y) produced by an additional unit of capital (K), holding labor (N) constant. To compare MPK and growth rates for capital (k) between Country A and Country B, we must analyze the function's properties.(a) The country with the lower initial value of k (Country B) will have a higher initial MPK compared to Country A, due to diminishing returns to capital. In this production function, MPK can be calculated by taking the partial derivative of Y with respect to K, which yields 0.3 K-0.7 N0.7. Since Country B has a lower initial k, this results in a higher MPK when the partial derivative is evaluated at B's lower K.(b) Since both countries are below their steady-state level k* and have identical savings rates and technologies, they will converge towards the steady-state. The country with the lower initial k (Country B) will experience a higher growth rate for k because it has more 'room' to grow to reach the steady-state, as suggested by the convergence hypothesis of the Solow model.It's important to note that these outcomes are the result of diminishing returns and convergence in the context of this specific model and the assumptions made about savings rates, technology, and other parameters being identical for both countries.