Question

Suppose President Obama’s “pro-green” budget encourages entrepreneurs to invest more in “green r and d.” The rate of technical progress increases from 1 to 3%. Using the Solow Growth Model, explain what happens to output per worker in efficiency units and consumption per worker in efficiency units. Does per capita output change as well? Explain.

Answer 1

Consider the given problem here the production function is given by, => y = f(k), where “y=output per worker in efficiency unit”, “k=capital stock per worker in efficiency unit” and “EN = effective number of workers”.

The change of the capital stock per worker in efficiency unit is given below.

=> ∆k = s*y – (n+d+g)*k, where “n=growth of the labor force”, “d=depreciation of capital stock” and “g=technological improvement”. At the steady state the change of the capital stock per worker in efficiency unit is zero, => ∆k = 0.

=> s*y = (n+d+g)*k. Consider the following fig.

Here the initial technological progress is “g1=1%”, => the initial steady state equilibrium is E1, where “i=s*y” and “(n+d+g1)*k” are equal, => the steady state “k=capital stock per worker in efficiency unit” is “k1” and “y=output per worker in efficiency unit” is “y1”. Now, as the technological progress increases from “g1=1%” to “g2=3%” the break-even investment line rotates to the upward side and at “k1” “(n+d+g2)*k= break-even investment” exceed the “i= investment per worker in efficiency unit”, => the change of the capital stock per worker in efficiency unit become negative, => ∆k < 0, => capital stock per worker in efficiency unit starts falling until the new steady state established.

At E2, the new steady state established, where the steady state “k=capital stock per worker in efficiency unit” is “k2” and “y=output per worker in efficiency unit” is “y2”. So, the increase in technological improvement decrease the “y=output per worker in efficiency unit”.

Now, the “c=consumption per worker in efficiency unit” is the difference between “y=output per worker in efficiency unit” and “i= investment per worker in efficiency unit”, that is “c = y-i”. A golden rule level of “k” represent a “capital stock per worker in efficiency unit” where “c=consumption per worker in efficiency unit” is maximum. If at k1 is more than the golden rule level of “k”, then an increase in technological improvement will increase “c”. Similarly, if at k1 is less than the golden rule level of “k”, then an increase in technological improvement will decrease “c”.

At the steady state equilibrium change of the capital stock per worker in efficiency unit is zero that is “∆k = 0”, => “k” is constant. So, the steady state output per worker in efficiency unit is also constant. Now, output per worker can be written as, => Y/N = y*E, where “E” is growing at the rate “g”.

The technological improvement increase “E” on the other hand it also decreases “y”, => the immediate effect on “output per worker” is ambiguous, but in the LR “output per worker” will increase.