Economic growth (Solow/AK)

Question 1

Stylized facts of growth, Kaldor 1961

Answer 1

1. Per capita output growths at a constant rate in the long run
   
   • But there can be low frequency changes
2. Physical capital per worker grows over time at a constant rate
3. Rate of return to capital is nearly constant
4. The ratio of capital to output is nearly constant
5. Shares of capital and labor in national income are constant
6. Growth rate of output per worker differs substantially over countries

Economy that exhibits the first 4 properties is said to be in a balanced growth path

Question 2

Solow model assumptions

Answer 2

1. Single homogeneous good that can be either invested or consumed
2. Closed economy (I=S)
3. No utility maximization
4. Population growths at an exogeneous and constant rate n
5. Technology level growths at an exogeneous and constant rate

Model is described by just a

• production function and
• capital accumulation function

Question 3

Production function definition

Answer 3

• Function of capital and labor

It exhibits:

• constant returns to scale on capital and labor
  
  • No rents under competitive markets
• It exhibits positive and diminishing marginal returns
  
  • Problem is concave
• Inada conditions
  
  • guarantee existence and uniqueness of the steady state

Question 4

Interest rate in solow model

Answer 4

In equilibrium in the capital markets, loans and capital must be perfect substitutes then r=(R-delta). Where R is the rental price paid to capital.

• Then in equilibrium f’(k)=r+delta

Question 5

instantaneous speed of convergence

Answer 5

measures the fraction of the gap between the initial point and the steady state that is erased in a given instant of time

• In the Cobb Douglas case the measure is beta=(1-alpha)(n+delta)

Question 6

absolute convergence

Answer 6

poor economies tend to grow faster than rich economies

• Solow model doesn’t imply this, what it says is that if two economies have the same underlying parameters then the poorest ones with display higher growth

Question 7

Golden rule of capital accumulation

Answer 7

savings rate that maximizes consumption in the steady state

if starting from a level of savings different from sg (golden rule savings rate) moving towards sg isn’t necessarily desirable

Question 8

moving from s lower than sg

Answer 8

• Initially consumption is a large proportion of income but the output is very low
• There is an initial decrease in consumption
• Then consumption increases monotonically until it reaches the steady state level
• We are sacrificing short run resources towards long run gains, whether this transition is desirable depends on the particular preferences of the consumers

Question 9

Hicks neutral technological progress

Answer 9

Ratio of marginal products remain unchanged for a given capital labor ratio i.e. y=Af(K,L)

Question 10

Steady state definition

Answer 10

rate of growth of capital per capita is constant

Question 11

moving from s>s^g to s^g

Answer 11

• too many resources are devoted to investment => consumption is lower than golden rule consumption
  
  • Initial jump=> consumption increases
  • Consumption decreases mononically until arriving to steady state
  • Consumption is greater in all periods

Here we are in dynamic ineficiency:

• Everyone can be better off by decreasing the savings rate

Question 12

Average speed of convergence

Answer 12

• Distance over time
• measures the fraction of the gap between the initial point and the steady state that is erased in a given interval of time t

Question 13

Harrod neutral (also known as labor augmenting)

Answer 13

Relative input shares (KF_K/LF_L) remain unchanged for a given capital labor ratio (Y=F(K,L*A))

Question 14

Capital accumulation equation

Answer 14

• Besides the model assumes an arbitrary rate of saving (as a proportion of the output)

Question 15

ahalf life

Answer 15

how long it takes for an economy to cover half the distance between the initial state and the steady state

Question 16

Solow neutral (capital augmenting)

Answer 16

Relative input shares LF_L/KF_K renain unchanged for a given capital labor ratio, i.e. Y=F(A*K,L)

Question 17

Implications of solow growth model

Answer 17

• Long run growth can’t come from capital accumulation
• Steady state is globally and asymptotically stable
• Differences in income between countries come from differences in the exogeneous parameters
• Investement and depreciation offset each other at the steady state
• Model is silent as to why some countries grow more than others
• consumption in steady state has an inverted u form
• steady state growth depends on exogeneous sources (technology growth)
• Model doesn’t determine the scale of the firm, but it determines the capital/labor ratio
• growth in this model is exogeneous, then growth in the steady state is independent from the savings rate and the technology level
• Continuous income per capita growth needs of continuous exogeneous technology growth

Question 18

AK model assumptions

Answer 18

y=Ak

• diminishing returns to capital are absent
• growth becomes endogeneous, it depends on the savings rate
  
  • sA>n+delta=> sustained growth per capita by means of continuous per capita accumulation
  • Growth rate depends in behavioral parameters s, n
  • No convergence prediction
• In general what we need for eternal growth is that the diminishing returns to capital have a lower bound that is large enough
• Technological progress continues to be exogeneous

Question 19

Conditional convergence

Answer 19

hypothesis that economies grow faster the further away they are from their own steady state

• solow is consistent with this. Poor countries then can grow at a slower rate than richer ones
• The variable that matters to determine rate of growth in the transition is the gap between the actual capital and the steady state value

Question 20

Characterization of steady state in solow growth model

Answer 20

• Steady state is globally asymptotically stable