Consider the Solow model with total factor productivity At constantly growing at rate g>0.

a. Determine the a) instantaneous impact on GDP per capita, b) instantaneous impact on consumption per capita, c) long-run impact on GDP per capita (i.e. compare the level of GDP per capita with and without the parameter change, in the long-run), d) long-run impact on consumption per capita (i.e. compare the level of consumption per capita with and without the parameter change, in the long-run), and e) impact on long-run GDP per capita growth rate of a one-time and instantaneous increase (jump) in productivity At, through a significant and non-repeatable invention. Assume the country begins at its “steady state value” of k* before this event occurs. Justify your answer by use of graph and/or equation. [Hint: this should not be considered a change in g, since productivity resumes growth at rate g after the one-time jump; it should be modeled as a onetime jump in At.]

b. Graph the path of yt and ct against time (or better yet, ln(yt) and ln(ct), which will be linear) for the event analyzed in part a.

c. Repeat parts a&b for a permanent, instantaneous increase in the growth rate of productivity, g.

Please show graphs, model and detailed working