Week 2 - Solow Model of Growth Flashcards
How is investment (i) defined in the Solow model?
i = sf(k), where s = the savings rate, and k = capital.
What are constant returns to scale?
If we increase factor inputs (K and L) by X%, total output will also increase by X%.
What is an intensive production function?
A production function written in “per worker” terms. For our purposes the intensive production will be:
y = f(k)
What conditions need to be satisfied to derive our intensive production function?
- Constant returns to scale.
- Positive, but diminishing marginal products of labour and capital.
- Inada conditions satisfied.
What is the formula for the change in capital stock?
Change in k = sf(k) - [delta]k
Why is the change in capital stock equation so central to this growth model?
It determines the behaviour of capital over time, which in turn determines many other endogenous variables, such as consumption and income, which implicitly depend on the
level of capital.
What is the steady state of capital?
A level of k, where investment is just enough to cover depreciation (ie. the change in capital equation = 0)
How does an increase in the savings rate affect the steady state of capital?
An increase in the savings rate, ceteris paribus, leads to an increase in k. Thus, the model predicts that higher k leads to higher levels of consumption and income in the long run. This is supported empirically.
What does “n” signify in the Solow model?
The rate of population growth. If capital remained the same, but population grew, the capital stock would have to be spread across more workers, leading to a fall in k.
How does population growth affect the steady state of capital?
As n increases, k* falls, ceteris paribus. This is because the breakeven level of capital ([delta] + n)k increases. Because of this, the model predicts countries with higher population growth experience lower consumption and incomes.
What are Kaldor’s 5 growth “facts”?
- Output per head, and capital stock per head show a rising trend.
- The capital to output ratio has remained fairly stable.
- Income per head is steadily rising.
- There is no systematic change in the profit rate.
- The shares of GDP going to capital and labour show no real systematic trend.
How does Solow’s model accommodate Kaldor’s growth facts?
- By assuming there is technological progress (A). This effectively augments labour, as if it increases the efficiency of workers.
What is the breakeven investment, taking into account g, the rate of growth of technological progress?
([delta] + n + g)k.
What is Solow’s residual?
If inputs are paid their marginal products, Solow’s residual measure the growth of income that is not explained by factor accumulation.
Solow’s residual = (alpha)*Ga , where alpha is labour’s share of GDP.
What is the golden rule level of capital?
The level of capital that maximised consumption. This will be where the tangent to our investment function is tangential to our breakeven investment line.
