Econ. 153a |
Fall 1966 |
C. Sims |

- The constant elasticity of substitution, or CES, production function has the form
- In the Solow model with Cobb-Douglas technology, determine
how output per worker at time
*t*is related to the rate of growth of output per worker at*t*under the following sets of assumptions. In each case, we assume that all economies were at their individual steady-state values of*k*just before*t*, but that these steady states differ across economies, and that just at*t*something happens to change the parameters of the model. - Steady states differed only because of differences in
*s*. Now*n*has increased by the same amount everywhere. - Steady states differed only because of differences in
.
Now
*s*has decreased everywhere. - Steady states differed only because of differences in
*A*. Now has increased everywhere.

.

As from below, this becomes a linear production function. As
, this becomes a "fixed coefficients"
production function in which there is only one efficient ratio of *K* to
*L*. As it can be shown (using l'Hopital's rule)
that it approaches a Cobb-Douglas form with share parameter . Using our standard notation for the Solow model, in which
the aggregate production function is

,

find the form of the equation for and solve for the steady-state as a function of the parameters (which now include the new parameter, ).