1. Consider a two-sector (RStD) growth model similar to the one discussed in class . Let L be the size of the labor force, and u 2 fraction of labour employed in research, and let the goods-production function be Y = F[K,(1n)EL], where E represents the effectiveness of labor in goods production. Ideas production is given by AE = g(uL)E, and capi- tal accumulation by AK = .91" 6K . There is no population growth. (a) (b) ((0 Suppose that uis constant. Use a Solow diagram to show that if the production F has constant returns to scale and diminishing marginal products, then there is a steady state where k = K/ (EL) is constant. Be sure to explain your reasoning (why are the assumptions needed in your diagram?).Show that in the steady state, output per Worker Y/ L grows at the same rate as E . Think of u as an exogenous variable. In what sense would this model be better than the Solow model with technical change for under- standing long-run growth? Also, what fact about the Solow residual discussed in the course can this model explain that the Solow model cannot? Suppose the economy is in a steady state. Explain how Y/ L and the growth rate AE/E change (and plot the time path of YXL) when: i. The fraction of labour in research increases permanently. ii. The population size L increases permanently . Historically, the countries with the fastest economic growth were of- ten relatively small countries such as England and Holland rather than larger countries such as India, Brazil, China, or Russia. Could this be a problem for the model? How could you explain that in the context of this model