Transition dynamics in the natural resources model. For the Solow model with natural resources in Section 10.1, show that K>Y does indeed converge to a constant. Calculate the value of this constant. Also, show that the growth rate of the capital-output ratio, and hence the growth rate of output per worker, declines or rises smoothly over time. (Hint: defi ne z = K>Y and analyze graphically the differential equation for z. This is a very useful tool in analyzing the Solow model more generally.)