Flashcards in Ch. 7 - Economic Growth I: Capital Accumulation and Population Growth Deck (47):
Why does supply and demand play a central role in the Solow model?
By considering the supply and demand for goods, we can see what determines how much output is produced at any given time and how this output is allocated among alternative uses.
What is the supply of goods based on in the Solow model?
The production function, which states that output depends on the capital stock and the labour force.
Y = F(K,L)
What is an assumption about the production function used in the Solow model?
Constans returns to scale.
zY = F(zK, zL) for any positive number z
What do production functions with C.R.S. allow us to analyze in the Solow model?
All quantities in the economy relative to the size of the labour force.
Y/L = F(K/L, 1)
How do we re-write the production function in the Solow model once we've set z=(1/L)?
y = f(k) where
y = Y/L
k = K/L
What is the slope of the production function designed to show in the Solow model?
MPK = f(k+1) - f(k)
What is the Solow growth model designed to show?
How capital stock, growth in the labour force, and advances in technology interact in an economy, and how they affect a nation's total output of goods and services.
How does the slope of the production function in the Solow model illustrate diminishing marginal product of capital?
The slope represents MPK, the fact that the slope gets flatter as k increases represents dimininshing product of capital.
What is the demand for goods based on in the Solow model?
From consumption and investment.
y = c + i where
y = output per worker
c = consumption per worker
i = investment per worker
How can we express the consumption function considering that the Solow model assumes that each year people save a fraction s of their income and consume fraction (1 - s)?
c = (1 - s)y where
c = consumption
s = saving rate where 0
How can we see what the new consumption function, developed in the Solow model, implies for investment?
Substitute (1 - s)y for c in the national accounts identity (demand for goods in the Solow model).
y = (1 - s)y + i
Rearrange the terms to obtain
i = sy
What does i = sy show?
That investment equals savings.
Which 2 forces influence the capital stock?
What is investment in the Solow model and what does directly influence?
Expenditure on new plant and equipment. It causes the capital stock to rise.
How can we express investment per worker as a function of the capital stock per worker?
Since i = sy, and y = f(k),
i = sf(k)
What is depreciation in the Solow model and what does directly influence?
The wearing out of old capital. It causes the capital stock to fall.
How do we incorporate depreciation into the Solow model?
We assume that a certain fraction of the capital stock wears out each year.
δ = depreciation rate
How do we express the impact of investment and depreciation on the capital stock in the Solow model?
Δk = i - δk
Δk = sf(k) - δk
Change in capital stock = Investment - Depreciation
When does k* reach steady state?
When i = δk.
What happens when i > δk?
Capital stock increases.
What happens when i < δk?
Capital stock decreases.
What are the 2 significant aspects of the steady-state level of capital?
-An economy at the steady state will stay there
-An economy not at the steady state will go there
What does the steady state level of capital represent?
The long-run equilibrium level of capital of the economy.
What is a direct result of growth in capital stock?
Growth in output
Which equation allows you to quickly find the steady state of capital in the Solow model?
0 = sf(k*)-δk*
k*/f(k*) = s/δ
What happens to an economy after its saving rate increases if it began at the steady state?
the sf(k) curve shifts upward.as s increases.
i, increase while δk* and k* remain the same, therefore i>δk. k* rises until the economy reaches the new steady state k* which has a higher capital stock and higher output.
How does the Solow model show that the saving rate is a key determinant of the steady-state capital stock?
If s is high, k* and y will also be high in ss.
If s is low, k* and y will also be low in ss.
What does the Solow model say about the relationship between saving and economic growth?
Higher s leads to faster growth in the Solow model but only temporarily (until it reaches a new steady state).
Maintaining a high s will also maintain a high k* and y, but it will not maintain a high growth rate forever.
What is said to have a growth effect?
Policies that alter the steady-state growth rate of income per person.
What is said to have a level effect and why?
A higher s because only the level of income per person - not it's growth rate - is influenced by the s in the steady-state.
What is the Golden Rule level of capital?
The steady-state value of k that maximizes consumption.
How can we find steady-state consumption per worker?
c* = f(k*) - δk*
Because capital stock is not changing in the steady-state, investment is equal to depreciation. substituting f(k*) for y and δk* for i in the national accounts identity c = y - i
What does the equation c* = f(k*) - δk* suggest? What is it telling us?
According to this equation, steady-state consumption is what's left of steady-state output after paying for steady-state depreciation.
On the one hand, more capital means more output, on the other hand, it also means more capital must be used to replace capital that is wearing out.
How is steady-state consumption depicted on a graph showing steady-state output and steady-state depreciation/investment as a function of steady-state capital stock?
Steady-state consumption is the gap between output and depreciation.
What happens if we increase capital stock, mathematically and graphically, if it's below the Golden Rule level in the Solow model?
An increase in the k raises f(k*) more than δk* so c* rises.
The production function is steeper than the δk* line, so the gap between the two curves - which equals consumption - grows as k* rises.
What happens if we increase capital stock, mathematically and graphically, if it's above the Golden Rule level in the Solow model?
An increase in the k raises f(k*) less than δk* so c* decreases.
The production function is flatter than the δk* line, so the gap between the two curves - which equals consumption - shrinks as k* rises.
How can we tell graphically when we've reached the Golden Rule level of capital?
At the Golden Rule level of capital, the production functions and the δk* line have the same slope, and consumption is at its greatest level.
How does a policy maker maximize the wellbeing of the individuals who make up the society?
By implementing policies which will eventually maximize consumption (reach the Golen Rule level).
How can we find the Golden Rule level of capital mathematically?
When MPK = δ or MPK - δ = 0
Because MPK is the slope of the production function and δ is the slope of depreciation.
What happens to c* if we increase capital when MPK>δ?
If MPK>δ, increases in k increase c*, so k* must be below the Golden Rule
What happens to c* if we increase capital when MPK
Why is it that the economy doesn't automatically gravitate toward the Golden Rule steady-state?
Because if we want any particular steady-state capital stock, such as the Golden Rule, we need a particular saving rate to support it.
Why is it more convenient to use the MPK-δ=0 identity than comparing steady-state levels of consumption?
Because it's relatively straightforward to estimate the MPK. By contrast, the second method requires estimates of steady-state levels of consumption at many different saving rates; such information is hard to obtain.
How should policymakers push the economy toward the Golden Rule level if it's starting with too much capital?
The policymakers should pursue policies aimed at reducing the rate of saving in order to reduce the capital stock.
How should policymakers push the economy toward the Golden Rule level if it's starting with too little capital?
The policymakers should pursue policies aimed at increasing the rate of saving in order to increase the capital stock.
What is the contrast between the cases of going toward the Golden Rule level when starting with too little vs too much capital?
When the economy begins above the Golden Rule, reaching the Golden Rule produces higher consumption at all points in time.
When the economy begins below the Golden Rule, reaching the Golden Rule requires initially reducing consumption to increase consumption in the future.