[Macro] Group 4 - Week 10: Solow model

In the basic Solow model, which of the following is treated as exogenous?

• Consumption level
• Saving rate
• Investment level
• Output level

Answer explanation

In the Solow model, the saving rate (s) is considered exogenous, meaning it is assumed to be fixed and not determined within the model. It plays a key role in determining investment since investment = s × output

What is the main objective of the Solow growth model?

• To predict short-run business cycles
• To determine equilibrium prices in markets
• To explain long-run differences in living standards across countries
• To analyze monetary policy in open economies

Answer explanation

The Solow model is a long-run growth model designed to explain why some countries have higher per capita incomes than others by focusing on capital accumulation, labor, and exogenous technological progress

According to the Solow model, when the economy reaches the steady state, what happens to output per worker (Y/L) if there is no technological progress?

• It increases over time
• It decreases over time
• It remains constant
• It fluctuates cyclically

Answer explanation

Without technological progress, the Solow model predicts that output per worker will stay constant in the steady state. Economic growth in per capita terms requires technological progress

Suppose a country increases its saving rate from 20% to 30% in the Solow model (with no technological progress). What will happen to capital per worker and output per worker in the long run

• Both will decrease
• Both will increase and keep increasing forever
• Both will increase to a higher level and then stabilize
• Nothing will change

Answer explanation

A higher saving rate leads to higher investment → more capital per worker → more output per worker. However, due to diminishing returns to capital, the economy eventually reaches a new steady state at a higher level of output per worker, but it doesn't grow forever

What is the role of technological progress in the extended Solow model?

• It increases the saving rate
• It reduces the depreciation rate
• It enables long-run growth in output per worker
• It makes investment less effective

Answer explanation

In the extended Solow model, long-run growth in output per capita is only possible through technological progress, which improves productivity even when capital per worker remains steady

Suppose the per-worker production function is y=k^0.5, the saving rate is s=0.2, and the depreciation rate is δ=0.05. What is the steady-state level of capital per worker?

• 4.0
• 16.0
• 9.0
• 25.0

Answer explanation

At steady state, investment per worker = depreciation per worker, so we solve for k at: 0.2k^0.5 = 0.05k

A country with a higher saving rate and a lower population growth rate ends up with a ___________ of output per effective labor in the _______.

• higher level, long run
• lower level, long run
• higher level, short run
• lower level, short run

Answer explanation

A higher saving rate increases investment and thus raises the steady-state capital per effective worker, which increases output per effective worker. A lower population growth rate reduces the rate at which capital gets diluted among workers, also raising the steady-state level.

During his presidency, Donald Trump proposed reducing legal immigration to “protect American workers.” In the Solow model with labor force growth n, a permanent reduction in immigration, all else equal, would lead in the long run to:

• Lower steady‑state output per worker, because fewer workers reduce specialization.
• Higher steady‑state output per worker, because capital per worker k* rises when n falls.
• No change in steady‑state output per worker, because n only affects total output growth.
• Higher growth rate of output per worker, because lower n raises technological progress.

Answer explanation

A decrease in population growth will shift the break-even curve downward, thus increasing the steady-state capital per worker. Therefore, the steady‑state output per worker increases.

A wave of factory automation increases worker productivity without changing capital per worker. Initially tech growth g=2%, widespread AI adoption raises g to 4%. What is the new long‑run growth of y?

• 4% per year
• 2% per year
• 6% per year

Answer explanation

In Solow with labor‐augmenting tech, y grows at rate g.

Vietnam launches a national digital education reform. Assume output per worker (y) grows from 3.2 to 3.84 in 10 years, while capital per worker (k) grows from 10 to 16. With y=Ak^1/2, estimate the change in total factor productivity (A).

• A increased by 20%
• A stayed the same
• A decreased by 5%
• A doubled

Answer explanation

Before: y=Ak^½ ⇒ 3.2=A⋅10^½ ​ ⇒ A=3.2/10^½ ​≈ 1.012 After: 3.84=A⋅16^½ ​⇒ A = 3.84/4 = 0.96 ⇒ ΔA=(0.96−1.012)/1.012 ≈ −5.1%