In the Solow model with no population growth (i.e., L is fixed), a rise in
[ Select ]
the depreciation rate
the level of productivity
leads to a higher steady-state capital stock, and a drop in
[ Select ]
the saving rate
the depreciation rate
leads to a lower steady-state capital stock.

Question

In the Solow model with no population growth (i.e., L is fixed), a rise in 
[ Select ]
the depreciation rate
the level of productivity
 leads to a higher steady-state capital stock, and a drop in 
[ Select ]
the saving rate
the depreciation rate
 leads to a lower steady-state capital stock.

BlackTom AI · Accepted Answer

In the Solow model with fixed labor, the steady-state condition equates investment per worker to depreciation per worker: s f(k*) = δ k*, where k is capital per worker, s the saving rate, δ the depreciation rate, and f(k) output per worker. With a productivity term A, output per worker is y = A f(k) (often A k^α for Cobb–Douglas). Start from the Cobb–Douglas specification y = A k^α (0<α<1). The steady state satisfies: s A k*^α = δ k*. Divide both sides by k*: s A k*^(α−1) = δ. Solve for k*: k*^(α−1) = δ/(s A) => k* = (s A / δ)^(1/(1−α)). This explicit expression shows dependence of k* on s, A, and δ. Complete reasoning and intermediate steps: - Rearranged steady-state condition to isolate k*: sA k*^α = δ k* → sA k*^(α−1) = δ. - Inverted exponent to solve for k*: k* = (sA/δ)^(1/(1−α)). - Because 1/(1−α) > 0, k* is increasing in s and A and decreasing in δ. Why the correct choices follow: - A rise in the level of productivity (A) increases the numerator sA, so (sA/δ)^(1/(1−α)) rises; hence steady-state capital per worker k* increases. Therefore the first blank is “the level of productivity.” - A drop in the saving rate (s) reduces sA, so k* falls; hence a lower saving rate leads to a lower steady-state capital stock. Therefore the second blank is “the saving rate.” Why the other options are incorrect: - An increase in the depreciation rate δ would lower k* (opposite direction), so it cannot be the factor that raises k* in the first blank. - A drop in the depreciation rate would raise k*, not lower it, so it cannot fill the second blank. Conclusion: the correct fills are “the level of productivity” and “the saving rate,” matching the provided answers.

类似问题

In this same Solow economy, you observe that GDP grows at a rate of 2.7 percent per year. Based on this information you know that the economy is _______.

An increase in leads to a higher steady-state capital stock, and a decline in leads to a lower steady-state capital stock.

Let 𝑠 ¯ be the investment rate, 𝛿 the depreciation rate, 𝐴 ¯ aggregate productivity (or TFP), 𝐿 ¯ the population, and 𝛼 the exponent on capital in the production function of a Solow economy. What is the steady-state level of investment per person 𝑖 ∗ ?

In the Solow model with population growth rate 𝑛 ¯ = 3 % , you know that total GDP grows at a rate of ________ percent in steady state.

Using the Solow model, if, in time 𝑡 = 0 , the initial capital stock is 𝐾 0 = 100 , investment is 𝐼 0 = 25 , and 𝑑 ¯ = 0.1 is the depreciation rate, capital accumulation from period 0 to period 1, i.e., Δ 𝐾 1 is:

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