Flashcards: Solow Model and Economic Growth — 55 cards

What does the Solow model explain in economics?

The proximate causes and mechanics of long-run economic growth and income differences.

What type of economy does the Solow model assume?

A closed economy with one good and no government sector.

Which inputs does the Solow model use in production?

Capital (K), labor (L), and knowledge or technology (A).

How does the Solow model treat technology across firms?

Technology is identical, publicly available, non-excludable, and non-rival.

What growth rates are assumed exogenous and constant in the Solow model?

Labor, technology, saving, and depreciation growth rates.

Over what time frame does the Solow model study economic growth?

Long-run growth over years rather than short-run movements over months.

From what capital level does the Solow model begin its analysis?

A low capital level moving toward a steady state.

How does the Solow model describe the path to steady state?

Through capital accumulation converging toward steady state.

What is the labor-augmenting technology production function formula?

$Y(t)=F(K(t),A(t)L(t))$

What does constant returns to scale imply for the production function?

$F(cK,cAL)=cF(K,AL)$ for every $c\geq 0$

How are output and capital per effective worker defined in efficiency units?

$y=\frac{Y}{AL}$ and $k=\frac{K}{AL}$

What is the reduced production function in terms of $k$?

$y=f(k)=F(k,1)$

What are the signs of the first and second derivatives of the reduced production function?

$f'(k)>0$ and $f''(k)<0$

What are the Inada conditions for the reduced production function?

$\lim_{k\to0}f'(k)=\infty$ and $\lim_{k\to\infty}f'(k)=0$

What is the Cobb-Douglas production function formula?

$F(K,AL)=K^\alpha(AL)^\beta$ with $0<\alpha,\beta<1$

When does the Cobb-Douglas function exhibit constant returns to scale?

When $\alpha+\beta=1$

What is capital intensity in production?

The amount of fixed or real capital relative to other factors, especially labor.

What characterizes firms in competitive markets regarding price?

They are price takers and cannot influence the market price.

How do households supply labor in the labor market?

They supply labor inelastically.

What equals the wage in the labor market?

The marginal product of labor.

When does the capital market clear?

When capital supply equals capital demand, $K^{supply}(t)=K^{demand}(t)$.

How is the net return on capital calculated?

As the gross return minus depreciation, $r(t)=r_K(t)-\delta$.

How does labor grow exogenously over time?

Labor grows according to $\dot L(t)=nL(t)$.

What is the formula for technology growth over time?

Technology grows according to $\dot A(t)=gA(t)$.

How is capital accumulation expressed in the model?

Capital evolves as $\dot K(t)=sY(t)-\delta K(t)$.

What does the saving rate s represent in capital evolution?

The saving rate s determines the fraction of output saved as investment.

What is the equation for capital per effective worker evolution?

Capital per effective worker evolves as $\dot k(t)=sf(k(t))-(n+g+\delta)k(t)$.

What does break-even investment offset to keep capital per effective worker stable?

It offsets population growth, knowledge growth, and depreciation.

What is the definition of break-even investment?

Investment required to maintain stable capital per effective worker by offsetting growth and depreciation.

When is the steady state reached in capital accumulation?

When $\dot k=0$, actual investment equals break-even investment.

What equation defines the steady-state condition for capital per effective worker?

$sf(k^*)=(n+g+\delta)k^*$ defines the steady state.

What happens to capital per effective worker if it is below its steady-state value?

Actual investment exceeds break-even investment and capital rises.

What happens to capital per effective worker if it is above its steady-state value?

Break-even investment exceeds actual investment and capital falls.

Why can't endless capital accumulation generate ever-increasing growth rates?

Because the production function is concave, marginal product of capital decreases as capital rises.

What effect does increasing the saving rate have on actual investment?

It shifts actual investment upward.

How does an increased saving rate affect capital per effective worker?

It permanently raises capital per effective worker to a new steady state.

What temporary effect does a higher saving rate have on output per worker?

It temporarily raises output per worker.

What is the formula for output per worker in terms of technology and capital?

Output per worker is $Y/L=Af(k)$.

What is the growth rate of output per worker?

It is $\frac{\textstyle \frac{d}{dt}(Y/L)}{Y/L}=g+\frac{\textstyle \frac{d}{dt}f(k)}{f(k)}$.

What does the growth rate of output per worker equal in the steady state?

It equals the technological growth rate $g$.

At the golden-rule steady state, what condition must the marginal product of capital satisfy?

It equals the slope of break-even investment: $f'(k^*)=n+g+\delta$.

What is the elasticity of steady-state output per effective worker with respect to saving in the Cobb-Douglas model?

It is $s\frac{\partial y^*}{\partial s}=\alpha_k(1-\alpha_k)$.

At what rate do capital, effective labor, and output grow on the balanced-growth path?

They grow at rate $n+g$.

At what rate do capital per worker and output per worker grow in the steady state?

They grow at rate $g$.

According to Robert Solow, what mainly drives economic growth?

Technological progress or productivity growth.

Why does the Solow model predict convergence among countries?

Because technology is a public good available to all countries.

What does the Solow model say about poorer countries catching up?

Poorer countries can catch up with richer countries due to shared technology.

How is the output-per-capita ratio between a rich and a poor country expressed?

$X=\left(\frac{y_a/L_a}{y_b/L_b}\right)=\left(\frac{K_a/L_a}{K_b/L_b}\right)^\alpha\left(\frac{A_a}{A_b}\right)^{1-\alpha}$.

How does the Solow model treat technology A and its growth rate g?

They are treated as exogenous.

What do endogenous growth models do differently with technology compared to the Solow model?

They make technology endogenous.

How is human capital treated in the Solow model?

It is included in technology A.

Which component is considered more important than human capital for explaining growth in the Solow model?

The knowledge component.

What motivates the development of models that endogenize technology A?

The limitations of the Solow model.

What additional features do models include beyond the Solow model?

Intertemporal household choices and broader capital including externalities.

Why might capital flows from rich to poor countries fail as predicted?

Because of institutional barriers and political risk.