Growth

Question 1

What are the main measures of living standards?

Answer 1

(Real) GDP per capita
Real GDP per capita in Purchasing Power Parity
Human Development Index (accounts for life expectancy, education, GNI per capita PPP)

Question 2

What is the relationship between growth and per capita GDP?

Answer 2

Plotting this for developed countries or the EU suggests a convergence but adding developing countries removes this, Asian countries seem to be converging but not African countries

Question 3

What is the formula for growth rate of GDP per capita?

Answer 3

%∆y_t+1 = (y_t+1 - y_t)/y_t

Question 4

What is the formula for constant growth?

Answer 4

x_t = (1+g_x)^tx₀

Question 5

How are logs used to deal with growth rates?

Answer 5

∆ln(x_t+1) = ln(x_t+1) - ln(x_t) ≈ ∆x_t+1 = g _x
So if z = x/y then g_z = g_x - g_y, if z = xy then g_z = g_x + g_y, and if z = x^a then g_z = a*g_x

Question 6

How can you approximate growth rates?

Answer 6

Rule of 70: if x grows at g% per year then x doubles in approximately 70/g yrs

Question 7

What are some costs and benefits of growth?

Answer 7

Benefits: health improvements, higher incomes, increased variety of goods and services
Costs: environmental problems, income inequality across and within countries, loss of certain types of jobs
Economists generally believe that benefits > costs for growth

Question 8

What are the changes the Solow model introduces to the neoclassical model?

Answer 8

K is not fixed, grows with investment and shrinks with depreciation
L is not fixed, grows with population
No G or T
Model is dynamic (deals with changes over time)
Consumption function is simplified

Question 9

What are the assumptions of the Solow growth model?

Answer 9

Neoclassical assumptions: firms are perfectly competitive profit maximisers, output is homogenous and produced by the neoclassical production function, K and L can grow over time, and technology/productivity is taken to be exogenous
Individuals consume and save a constant fraction of income
Population = labour force, this is at a fixed level, productivity doesn’t change and so can be set to 1

Question 10

How does the Solow growth model adjust the neoclassical production function?

Answer 10

Because of CRS, the multiplier can be set to 1/L so Y/L = F(K/L, 1) so y = F(k, 1) = f(k)
Therefore the model predicts that income per person depends on productivity and capital per person

Question 11

How does the Solow growth model relate saving, consumption, and investment?

Answer 11

Y = C + I (in aggregate terms) so y = c + i (in per person terms)
s - savings rate (exogenously given)
c = (1 - s)y so saving per worker = y - c = sy
i= y - c = sy = sf(k)

Question 12

How does capital change in the Solow growth model?

Answer 12

change in capital stock per person ∆k = investment i - capital depreciation ∂k (where ∂ is a constant fraction)
Since i = sf(k), ∆k = sf(k) - ∂k

Question 13

What are the equations and endogenous variables of the Solow growth model?

Answer 13

Endogenous variables (all per capita): k, y, c, i (all depend on first)
y = f(k)
∆k = i - ∂k
c + i = y
i = sy
K and L aren’t considered as MPL & MPK would fix them so the dynamics of the model wouldn’t change

Question 14

Where is the Solow model steady state and how is it represented graphically?

Answer 14

The steady state is where ∆k = 0 therefore sf(k) = ∂k
On a y against k graph an increasing concave line can be drawn for sf(k) and a similar higher line for f(k), with the distance between them being consumption, the height of the first being investment, and the height of the second being income
On a graph of i and ∂k against k, depreciation ∂k is a straight upwards sloping line which will intersect with sf(k) at one point which is the steady state level of capital k*, below this point there is more investment per person than depreciation per person and above this point there is more depreciation than investment, both of which push the level of capital towards the steady state

Question 15

What is the solution to the Solow model steady state level of capital and output?

Answer 15

Since the Cobb-Douglas production function means y = f(k) = Ak^a and the steady state condition is sf(k) = ∂k, these can be combined to get sA(k)^a = ∂k so k* = A^1/(1-a)(s/∂)^1/(1-a) and y* = = A^1/(1-a)(s/∂)^a/(1-a)

Question 16

Why does the economy reach a steady state in the Solow model?

Answer 16

Investment and depreciation increase and decrease the capital stock respectively at a constant rate but investment has diminishing returns so the rate at which production and thus investment rise is smaller as the capital stock is larger

Question 17

What does the Solow model say about long run growth?

Answer 17

Since a steady state level of capital is reached, capital accumulation is not the engine of long run economic growth, the model predicts that there should be no long run growth in output per person but economies appear to grow continually over time

Question 18

How can comparative statics be carried out on the Solow model?

Answer 18

On a plot of i, ∂ against k, if the rate of depreciation increases then the ∂k line pivots anticlockwise which results in a lower k, if savings rate increases then the sf(k) line gets higher so k increases

Question 19

What does the Solow model predict about the relationship between economic and population growth?

Answer 19

Population growth can lead to aggregate economic growth but not long run economic growth per person (therefore not living standards) due to the diminishing returns of capital per person
Mathematically, Y* = y*L so g_Y* = g_y* + g_L = 0 + n

Question 20

How do you derive the fundamental equation of the Solow model when population growth is factored in?

Answer 20

∆K = sF(K, L) - ∂K
In per person terms: (∆K)/L = sF(K, L)/L - ∂K/L = sf(k) - ∂k
Since ∆ approximates a derivative: ∆k = ∆(K/L) = (L∆K - K∆L)/L² = (∆K)/L - (K/L)*((∆L)/L) = (∆K)/L - kn
Using previous equation: ∆k = sf(k) - (∂+n)k

Question 21

What are the two components of the fundamental equation of the Solow model?

Answer 21

sf(k) is the actual investment, (∂ + n)k is the break-even investment which is the level of investment required to keep capital per worker constant

Question 22

How can you calculate the change in population growth?

Answer 22

Change in population growth = fertility - mortality + migration

Question 23

What does the Solow model predict about different savings rates?

Answer 23

Different values of s lead to different steady states, higher s leads to higher k* which leads to higher y*

Question 24

What is the golden rule steady state and where does it occur?

Answer 24

The steady state where consumption is maximised, corresponding to a level of capital k_gold*
c* = y* - i* = f(k) - (∂ + n)k is maximised where its partial derivative wrt k* equals 0 so f’(k*) = MPK = ∂ + n

Question 25

What is required for an economy to reach the golden rule steady state?

Answer 25

Policy intervention to adjust the savings rate to the level that would result in the golden rule steady state

Question 26

How is the transition to the golden rule steady state graphically represented?

Answer 26

Plot lines for y, c, and i against time
When k* > k_gold* savings need to decrease so income falls, investment jumps down then falls a little, consumption jumps up then decreases towards a level higher than the initial level
When k* < k_gold* savings need to increase so income increases, consumption jumps down then increases to a higher level than initially, and investment jumps up then continues to increase

Question 27

What is the difference between dynamic efficiency and dynamic inefficiency in the Solow model?

Answer 27

When the savings rate is lower than the golden rule level the economy is dynamically efficient as a temporary drop in living standards (consumption) is required to achieve a higher level of consumption
When the savings rate is higher than the golden rule level the economy is dynamically inefficient as a high level of consumption can be achieved without any decrease in standards of living

Question 28

What is the formula and graph for the growth rate of capital per person?

Answer 28

g_k = (∆k)/k = sf(k)/k - (∂ + n)
First term changes over time but second term is constant
On a plot with k on the x axis, sf(k)k is a convex decreasing line and (∂ + n) is a horizontal line

Question 29

What are the predictions of the Solow model related to the growth of capital per person?

Answer 29

Countries will converge if they share s, n, ∂ (conditional convergence) and there should be a negative relationship between initial income and growth, however these variables are unlikely to be the same across countries and observations support the idea that poorer countries are closer to their lower steady state levels of output and so have lower growth

Question 30

What is the augmented Solow growth model?

Answer 30

Considering labour-augmenting tech progress measured in labour efficiency E so LE is a measure of effective workers
Y = F(K, LE) = E^1-aK^aL^1-a where E^1-a accounts for TFP instead of A

Question 31

What is the fundamental equation of the augmented Solow model?

Answer 31

∆k = sf(k) - (n + ∂ + g)k where g is the rate of improvement of labour efficiency (∆E)/E and f(k) is the production function in terms of effective workers

Question 32

What is the break-even investment in the augmented Solow model?

Answer 32

The investment needed to replace depreciating capital (∂k) plus that needed to provide capital for the new workers (nk) plus that needed to provide capital for the more effective workers (gk)

Question 33

Where is the golden rule steady state for the augmented Solow model?

Answer 33

Where MPK - ∂ = n + g, i.e. where the marginal product of capital net of depreciation equals the population growth rate plus the rate of technological progress

Question 34

What does the augmented Solow model conclude about economic growth?

Answer 34

Capital and output per effective worker will not increase after the steady state, output per worker Y/L = yE will increase at the exogenous rate of technological progress g, and total output Y = yEL will increase at a rate of n + g

Question 35

How do you evaluate the rate of saving in the augmented Solow model?

Answer 35

If MPK - ∂ > n + g then s is lower than the golden rule level, if < then s is too high

Question 36

What are policies to improve standards of living based on the augmented Solow model?

Answer 36

Increase the saving rate: reduce capital gains or corporate income or estate tax as these discourage saving, replace income tax with a consumption tax, improve incentives for retirement savings accounts
Improve technological progress: patent laws, tax incentives for R&D, grants for research, industrial policy