Solow Model Exercise

1. The constant elasticity of substitution, or CES, production function has the form

.

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, ).

2. 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.
1. Steady states differed only because of differences in s. Now n has increased by the same amount everywhere.
2. Steady states differed only because of differences in . Now s has decreased everywhere.
3. Steady states differed only because of differences in A. Now has increased everywhere.