a. Increased productivity immediately boosts output. Initial effects on saving and capital depend on investment responses. b. The economy converges to a new steady state with higher output and capital per worker, reflecting the enhanced productivity.
a. Immediate Impact on Output, Saving, and Capital Depreciation and Dilution:
- Output: There will be an immediate increase in output since productivity (A) is a factor in the Solow model's output function.
- Saving: Initially, saving may not change significantly unless there are adjustments in investment behavior in response to the increased productivity.
- Capital Depreciation and Dilution: With the increase in productivity, the rate of capital depreciation may decrease, and there might be a temporary decrease in dilution (if the population growth rate remains constant).
b. Convergence to a New Steady State:
- The economy will converge to a new steady state. As productivity (A) increases, the new steady state will have higher levels of output and capital per worker.
- Dynamics: Initially, the economy will experience a period of growth as it moves towards the new steady state. During this transition, both output per worker and capital per worker will increase.
- Output per Worker: It will increase during the transition to the new steady state, reflecting the higher productivity level.
- Capital per Worker: It will also increase during the transition due to the initial accumulation of capital resulting from increased productivity.
In summary, the immediate impact of an increase in productivity is higher output, and over time, the economy will adjust to a new steady state with increased levels of output and capital per worker. The transition involves a phase of growth as the economy converges to the new equilibrium.
The complete question is:
Assume that an economy is in its steady state according to the Solow model with a constant productivity level. In addition, assume that the economy experiences an increase in its productivity (Say, for example, that A grew from 1 to 1.5). a. What will be the immediate impact on output, saving and capital depreciation and dilution? b. Will the economy converge to the same steady state? If it converges to a new steady state, describe the dynamics, and what happens to output per worker and capital per worker in the new steady state.