Consider the Solow model, whose key equations are given as follows:N’= (1 + n)NS = sYY = zK^aN^(1?a)K0 = (1 ? d)K + Iwhere N is employment or population; n is the population growth rate; S is aggregate savings; Y is aggregateoutput; z is total factor productivity; K is the aggregate capital stock; d is the depreciation rate; and I isaggregate investment. Assume 0 < a < 1.Suppose that the economy starts o? in steady state, and then there is a sudden increase in total factorproductivity at year 2015.(a) Show, using diagrams, the inital level of capital per worker and how capital per worker and outputper worker will change in the short run and the long run.(b) Show, using diagrams, the evolution of the natural log of aggregate output and aggregate capital.Start with the initial state, then show what happens in time in the short run and the long run.