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Answer :
Final answer:
The steady state capital per worker is determined by the equation where the capital depreciated is offset by savings, and an increase in the growth rate of technology could influence both capital and consumption levels per worker in the steady state.
Explanation:
To solve for the steady state level of capital per worker (denoted as k*) in this economic model, we rely on the given equation where the amount of capital depreciated is exactly offset by the amount saved. The steady state condition is given by k* = (sAƒ(k*)) / (δ), where s represents the savings rate, A represents the technology factor, f(k*) is the production function with respect to capital per worker, and δ is the depreciation rate. Substituting these into the equation we can solve for k*.
In regards to the effect of an increase in the growth rate of technology (denoted as g¯) on the steady state capital per worker, an increase in g¯ would, ceteris paribus, increase the efficiency of the capital and encourage more investment, potentially increasing the steady state capital per worker.
As for the steady state consumption per worker, which is typically found by subtracting investment from output (c* = f(k*) - δk*), an increase in g¯ may lead to higher production which might result in higher consumption per worker in the steady state; however, the relationship is more complex and could depend on other variables such as the savings rate and the effect of increased technology on the depreciation rate.
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