Question

Slowdown in productivity growth

Consider the following two scenarios:

i) The rate of technological progress drops permanently.

ii) The savings rate drops permanently.

a) Analyse graphically, what is the impact of each of these scenarios on economic growth in the next five years (short run)?

b) Over the next five decades (long run)? Discuss the effects on both growth rates and output levels.

Answer 1

a).

Consider the given problem here the production function is given by, => Y = K^a*(AL)^1-a, where “A” be the technology parameter. So, as “A” increases “Y” increases and vice versa. Now, let’s assume that “A” is growing at the rate “g”. Consider the following fig.

So, here “E” be the steady state equilibrium point where “s*y” cut the break even investment “(n+d+g)*k”. So, the steady state equilibrium “capital stock per effective worker” is given by “k*”and the “steady state equilibrium output per effective worker” is given by “y*”. Now, “k*” is constant, => the growth of “y*” is “zero”. So, the output the economy as a whole is given by.

=> Y = (y*)*(AL), => “Y” is growing at the rate “n+g”, => Now, if “A” slow down, => the growth rate of “Y” also slowdown, => the in the SR as well as in the LR the growth rate of “Y” decreases.

Consider the following fig shows the change in savings rate.

So, here the initial savings rate was “s1” and “E1” be the equilibrium, => the capital per effective worker and output per effective worker are given by “k*1”and “y*1” respectively. Now, as the savings rate decreases, => the “s*y” line get flatter, => the new equilibrium is “E2”, => both the “k*” and “y*” decreases. Now, once the new equilibrium will established, => “k” and “y” become constant.

So, here output of the economy as a whole is given by “Y=y*AL” is growing at the rate “n+g”. So, as “s” decreases, => “y” decreases temporarily, => the growth rate of “Y” is less than “n+g” and when “y” constant => the “Y”is growing at the rate “n+g”, as before. So, in the SR the growth rate of decreases and in the LR the growth rate of “Y” come back to the original level.