PROBLEM SET 3, MACROECONOMICS: POLICY, 31E23000, SPRING 2017

Transcription

1 PROBLEM SET 3, MACROECONOMICS: POLICY, 31E23000, SPRING Ue the Solow growth model to tudy what happen in an economy in which the labor force increae uddenly, there i a dicrete increae in L! Aume that the economy i initially at the teady tate! What happen to the income per capita in the hort run? What happen to the growth rate? What happen to the long run income per capita? A: Note that the quetion i about a dicrete, one time increae in the population/labor force ize, not about a change in the population growth rate. Thu we aume that thee new people have the ame birth rate a the original people. On impact, ince the current capital tock i given by pat deciion, the capitallabor ratio decline. In Figure 2 I aume that initially the economy i in the teady tate (note alo that the analyi applie to all incarnation of the Solow-model) capital-labor ratio decline from k to k. Two thing happen on the impact: the growth rate increae and the income per capita decline. The economy begin to converge back to it initial equilibrium, the one-time increae in population doe not have any effect on the long run equilibrium. But notice that during the whole growth rate (dk/dt)/k SugarSync/Luennot/Macro2016/PS4F2.pdf k -α n+δ k' k* k 1

2 2 PROBLEM SET 3, MACROECONOMICS: POLICY, 31E23000, SPRING 2017 SugarSync/Luennot/Macro2016/PS4F3.pdf adjutment proce income per capita i lower than it would have been without the udden inflow of the people. Note that thi i an example of a cae where increaed growth and decline in income can be oberved imultaneouly. 2. During the lat year there ha been a lot of dicuion about increaed income inequality, poibly partly due to technological change. Some of the change can then be crudely captured in the imple Solow growth model by auming that labor hare in aggregate income ha declined, i.e. α ha declined. To tudy the implication for growth of thi decline, aume that the economy i initially in the teady tate with higher α and tudy both the hort and long term impact of a decline in α! What would happen, if realitically alo imultaneouly the rate of technological progre x increae! A: Let u firt look at what happen if the labor hare alone decline. Figure 3 tell the tory. The decline in the labor hare i equivalent to α becoming maller, and thereby 1 α becoming larger. Thi implie that at any capita-labor-ratio the aving curve hift up: Increae in the capital hare i equivalent to capital becoming more productive (the marginal product of capital increae at given capital-labor ratio), thu increaing output per capita. If the economy i initially in the teady tate there will be a new period of growth to reach the higher capital-output ratio, in other initial ituation there i alo a temporary boot in the growth rate. Let u now move to the cae where alo the rate of productivity growth, x, increae imultaneouly with the technological change reducing labor hare. The

3 PROBLEM SET 3, MACROECONOMICS: POLICY, 31E23000, SPRING line (δ + n + x) ˆk rotate upward, Figure 4 how what happen. I have drawn the cae where the increae in the rate of productivity growth reduce the capitalefficient labor ratio. There i therefore a period of degrowth in the ene that capital tock i being effectively decumulated, it eem a if the role of phyical capital a a ource of growth diminihe or diappear. There i naturally growth becaue the labor productivity grow. The mot intereting item i what happen to (real) wage. A we aume the economy to be competitive, we know that the wage equal the marginal product of labor. A the production function relevant for thi cae i Y t = Kt 1 α (A t L t ) α the wage rate i (1) w t = αa t K 1 α t (A t L t ) α 1 = αa t ˆk t 1 α, ˆk K AL Taking a derivative of thi with repect to the labor hare α give (in doing thi you may want to ue the fact that ˆk 1 α t = e (1 α)lnˆk t ) (2) w α = [1 α (1 α)] A 1 α t ˆk t Thi i poitive (a α (1 α) < 1 for α < 1) implying that the impact effect of a reduction in the wage hare i a decline in real wage. Real wage alo decline further if the rate of productivity growth reduce the teady tate capital intenity of production. With a change in the labor hare alone the long run capital intenity increae counteracting the immediate effect. If you want, you can try whether the effect i trong enough to lead to an increae in the real wage by uing the formula for the teady tate capital intenity. And we mut remember that productivity growth definitely goe on and increae the real wage in the end. 3. In dicuion about Finnih economy one very commonly expreed view i that Finnih labor market are too rigid. An implication of thi view i that with more flexibility in the labor market the equilibrium unemployment rate would decline. So aume there i an equilibrium unemployment rate u e. Thu, if N = total labor force, then labor input i L = (1 u e ) N. Uing the Solow-Creative Detruction model introduced in the Lecture and elaborated in the textbook, what happen to the innovation rate if the equilibrium rate of unemployment decreae? To carry out thi analyi, you hould formally derive what happen to the Solowrelationhip relating the innovation rate to the output per productivity adjuted labor force? To make thi eay, aume that the unemployed receive unemployment benefit (paid from the income generated by capital and the employed) but they ave from the benefit at the ame rate a the employed peron. Do you have any idea on why the reduction in unemployment rate could affect directly alo the Schumpeterian relationhip etablihing a poitive relationhip between rate of innovation and the market ize, i.e. hift the relationhip to the left or right? A: Thi i quite a peculative quetion. To begin with, notice that in term of the Solow-model the decline in the unemployment rate i exactly the ame thing a the one time increae in the labor force tudied above in Problem 1. What thi mean i that there i no impact on the Solow-curve for the model where the rate of innovation and output per productivity adjuted labor force are determined

4 4 PROBLEM SET 3, MACROECONOMICS: POLICY, 31E23000, SPRING 2017 SugarSync/Luennot/Macro2016/PS4F4.pdf imultaneouly by the Solow-curve and the Creative Detruction (Schumpeter) - curve. Given the aumption made, unemployment doe not change anything ele in the model but the ize of the labor force for any given level of population, the labor force grow by the ame percentage a the population.. The Solow-curve can be derived from the teady tate condition requiring that the ratio of capital relative to productivity adjuted labor force remain contant (3) (k ) α = x + n + δ ( k = x + n + δ Thu, the rate of unemployment doe not have any impact on thi teady tate capital. Thi mean that it doe not have any impact on the teady tate income per productivity adjuted income, either: (4) ( Y A (1 u e ) L y = (k ) 1 α = x + n + δ ) 1 α ) 1 α α Thi clearly give a negative relationhip between the income (market ize) and the rate of innovation x. How doe the decline in the unemployment rate affect the Schumpeter-curve? Frankly, I do not have any idea. Like the Solow-curve, it i a long-run relationhip and it i hard to ee why there hould be any impact from unemployment rate on the relationhip. But the reaon why I gave thi problem i that there may be

5 PROBLEM SET 3, MACROECONOMICS: POLICY, 31E23000, SPRING x SugarSync/Luennot/Macro2017/Lecture 6/PS3F3.pdf Equilibrium unemployment, innovation and output Schumpeter D B Solow A 0 C ome intereting medium run dynamic coming from the permanent change in the unemployment rate, in thi cae from the reduction, but remember that thi i highly peculative. See the next figure and recall the reult from the firt problem: On the impact when the mployment rate decline the labor force grow and the output per worker decline. The initial equilibrium i at point 0, now it move to point A. Thi lead, from the Schumpeter-curve, the rate of innovation, to point B. But thi lower rate of innovation (and productivity growth) increae the output, to point C. But thi increae the rate of innovation, to D, reducing the income,.... Thu, the reult i ome ort of a cycle, not a buine cycle, but medium term or even longer term cycle. But now we have entered dangerou water of long cycle with a long hitory. The olution are due by March 15 at 12:00 AM hour!