(Solved): Consider the standard Solow model. The expression for output per worker and the dynamics of capita ...

Consider the standard Solow model. The expression for output per worker and the dynamics of capital per worker are given by the following expression: \[ \begin{array}{c} y=A k^{\alpha} \\ \Delta k=s y-\delta k \end{array} \] where \( \delta>0 \) is the depreciation rate of capital. (a) Using a Solow diagram, what is the effect of an increase in productivity A on steady state capital? (label the axes and mark the initial and the final steady state level of capital) (b) Find an algebraic expression for the steady state capital per worker. (c) What happens to steady state output and consumption after a positive productivity shock? Justify your response. 3 (d) If the real wage equals the marginal product of labor, what is the growth rate of the real wage in steady state?