Suppose that you have a standard Solow model without growth. The central equation governing the dynamics of the level of capital is given by Kt+1 = (1 − 8)K₂ + It. In terms of capital per worker, the central equation is given by kt+1 = i + (1 - 6)kt. (a) Suppose that the economy initially sits in a steady state in terms of the capital stock per worker, k = k*, and the total number of workers Ē. Suppose that, at time t, the number of workers doubles (say, due to an influx of immigrants). The number of workers is expected to remain forever thereafter constant at this new higher level, i.e. Lt+1 = 2ī. Graphically analyze how this will impact the steady state capital stock per worker and the dynamics starting from an initial capital stock. (b) Draw diagrams plotting out how capital, output, and the real wage ought to respond dynamically to the permanent increase in the workforce. (z-axis is time and y-axis is the corresponding variable)