Chapter 9 Flashcards
What is the purpose of the Solow Model with Embedded Technological Progress? What is the key equation?
To analyze long-run growth per effective worker by including both population growth (n) and technological progress (g). It adjusts capital and output per effective worker:
Effective labor = At Lt
Per effective capital = kt = KtAt Lt
Per effective output = yt = YtAt Lt
Solow Model = Δkt=kt+1−kt=sf(kt)−(δ+n+g)kt, This shows how capital per effective worker evolves, accounting for: Saving (s), Depreciation (δ), Population growth (n), Tech progress (g)
In the Solow model with embedded technological progress, what are the steady-state growth rates of output and capital per effective worker, per worker, and in total? Why do they differ?
Steady State Growth Rates:
Per effective worker output yt, capital kt, growth rate: 0. At steady state, effective worker variable are constant
Per worker output yt , capital kt, growth rate: g. Tech progress At grows at rate g: yt = Atyt
Total output Yt, capital Kt, growth rate: n + g, includes growth of population n and tech g: Yt = Ntyt
Welfare depends on per worker variables, not total values → focus on yt and kt
What happens in the Solow Model when the technological growth rate (g) increases?
Are people better or worse off? Draw Graph
In the new SS equilibrium, the levels of per effective worker output and per effective worker capital will be lower. Since welfare depends on per worker consumption/output → People are worse off.
What happens in the Solow model when the population growth rate (n) increases? How does it affect steady-state per effective worker capital/output and overall well-being?
In the new SS equilibrium, the levels of per effective worker output and per effective worker capital will be lower. Since welfare depends on per worker consumption/output → People are worse off.
What is the difference between exogenous and endogenous growth models?
Exogenous Growth Model: In models like solow embedded model, the continuous growth of the economy (growth rate of technological progress), g, is determined exogenously (outside the model)
Endogenous Growth Model: Models that create the continuous growth of the economy is determined by (within the model)
What is the main insight of the AK Model in endogenous growth theory?
The AK Model assumes output is proportional to capital: Yt = AKt. Substituting in the solow equation,IfsA>(n+δ), the capital and output grow indefinitely.Growth is endogenous—determined within the model through savings and productivity.
What does the AK Model say about convergence between poor and rich countries? Use examples to explain.(Convergence vs Leapfrogging)
Formula: ktkt = sA - (n + δ)
No Convergence Example: Both countries have the same s, A, n, and δ, They grow at the same rate (2%), No convergence, even if one starts richer.
Leapfrogging Example:Poor country: higher s and A,Rich country: lower s, A, and higher growth drag,Poor country grows faster (3% vs. 1%), Leapfrogging: the poor country can overtake the rich one.
What is the Barro Endogenous Growth Model and how does it lead to sustained growth?
The Barro Model includes both physical capital (K) and human capital (H) in the production function: Y=βKαH1−α. Assumes constant returns to scale and diminishing returns to each factor.By arbitrage (equalizing returns on K and H), we set: MPK=MPH, H= 1 - ααk, Substituting into the production function leads to: Y = AK
What distinguishes the Romer Model from the Solow Model in explaining long-run economic growth?
The Romer Model introduces ideas (knowledge) as a key driver of growth, alongside labor and objects (output):
Solow Model: Capital + Labor → Objects (Output)
⤷ Constant returns to scale in objects
Romer Model:
Ideas + Labor → Objects
⤷ Ideas are produced using labor and feedback into production
⤷ Constant returns to scale in objects alone
⤷ Increasing returns to scale when combining ideas + objects
In the Romer Model, what are the key differences between ideas (knowledge) and objects (output)? Why does this matter for economic growth?
In the Romer Model of endogenous growth, ideas (knowledge) are considered virtually infinite and are treated as public goods because they are nonrival and nonexcludable meaning one person’s use doesn’t diminish another’s, and no one can be prevented from using them. As a result, unregulated markets tend to underproduce ideas, making them underprovided. To ensure adequate innovation, ideas must become excludable through mechanisms like intellectual property rights (e.g., patents and copyrights). In contrast, objects (outputs) are finite and are private goods, which are both rival and excludable. This distinction is crucial because while markets efficiently allocate objects.
Compare Growth Accounting and Formulas, Romer vs. Romer-Solow
Romer Slow Model:
Output: Yt=AtKαtLyt1−α
Growth of Output:gY = g1−α
Growth of per worker output: gy = gY = g1−α
Romer Model:
Growth of per worker output: gy = g
Comparison: Romer Solow has higher growth g < g1−α. Romer-solow grows faster because of direct and indirect effects. Direct effect: More knowledge (TFP↑) raises output directly. Indirect effect: more knowledge increases capital productivity raising capital stock (k).
What is the output along BGP (Balanced Growth Path)
Formula: yt=(1−ℓ)A011-α ( szℓL1- α +δ )α1-α (1+zℓL)t1-α
BGP (Balanced Growth Path): A state where all variables grow at constant rates.This formula shows how per worker output evolves over time under the Solow-Romer model.Split into: Level effect (affects initial output), Growth rate effect (affects long-run slope).
What are transition dynamics in the Romer-Solow model, and how do they differ from the Romer model?
Transition dynamics refer to how an economy adjusts toward its balanced growth path (BGP) over time. The Romer-Solow model shows transition dynamics due to diminishing returns to capital unlike the Romer model, which immediately jumps to a new BGP. If an economy is below BGP, it grows faster. If it is above BGP, it grows slower.
Example: If the saving rate s↑, the economy is now below the new balanced growth path. The growth of per worker output is immediately higher. The slope of the output path is steeper than the balanced growth path. But the growth rate finally falls back to the original rate.
Solow model explains transitional dynamics from one balanced growth path to another, the Romer model explains the balanced growth path.
