# Suppose President Obama’s “pro

Suppose President Obama’s “pro-green” budget encouragesentrepreneurs to invest more in “green r and d.” The rate oftechnical progress increases from 1 to 3%. Using the Solow GrowthModel, explain what happens to output per worker in efficiencyunits and consumption per worker in efficiency units. Does percapita output change as well? Explain.

Answer:

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

The change of the capital stock perworker 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 changeof the capital stock per worker in efficiency unit is zero, =>∆k = 0.

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

Here the initial technologicalprogress is “g1=1%”, => the initial steady state equilibrium isE1, where “i=s*y” and “(n+d+g1)*k” are equal, => the steadystate “k=capital stock per worker in efficiency unit” is “k1” and“y=output per worker in efficiency unit” is “y1”. Now, as thetechnological progress increases from “g1=1%” to “g2=3%” thebreak-even investment line rotates to the upward side and at “k1”“(n+d+g2)*k= break-even investment” exceed the “i= investment perworker in efficiency unit”, => the change of the capital stockper worker in efficiency unit become negative, => ∆k < 0,=> capital stock per worker in efficiency unit starts fallinguntil the new steady state established.

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

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

At the steady state equilibriumchange of the capital stock per worker in efficiency unit is zerothat is “∆k = 0”, => “k” is constant. So, the steady stateoutput per worker in efficiency unit is also constant. Now, outputper worker can be written as, => Y/N = y*E, where “E” is growingat the rate “g”.

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