An economy has a cobb-douglas production function:
Y=K^(a)(LE)^(1-a)
The economy has a capital share of 1/3, a saving rate of 24%, adepreciation rate of 3%, and a rate of population growth of 2%, anda rate of labor-augmenting technological change of 1%. It is insteady state.
a) At what rates do total output, output per worker, and outputper effective worker grow?
b) solve for capital per effective worker, output per effectiveworker, and the marginal product of capital.
c) does the economy have more or less capital than at the GoldenRule steady state? how do you know? To achieve the golden rulesteady state, does the saving rate need to increase ordecrease?
d) suppose the change in the saving rate you described in part coccurs. during the transition to the golden rule steady state, willthe growth rate of output per worker be higher or lower than therate you derived in part a? after the economy reaches its newsteady state, will the growth rate of output per worker be higheror lower than the rate you derived in part a? explain youranswers.
