economic growth

Question 1

what is the extensive form of production function?

Answer 1

Y = F(K,L) where K is capital , L is labour and Y is real output

Question 2

what are the assumptions that economists make about the production function as follows?

Answer 2

output increases as either factor or both factors increase
if one factor remains fixed, increases of the other factor yield smaller and smaller output gains
if both factor rise by the same percentage, output rises by this percentage

Question 3

what is the marginal product of capital?

Answer 3

the marginal product of capital is the output added by adding one unit of capital

Question 4

what are constant returns to scale?

Answer 4

a production function that has constant returns to scale if raising all inputs by a given factor raises output by the same factor

Question 5

what is the cobb douglas production function?

Answer 5

Y= A x K^b x L^(1-b)

Question 6

what is growth accounting?

Answer 6

it tries to link observed income growth to factors that enter the production function without asking why those factors developed the wat they did. that question is left to growth theory. it wishes to arrive at some hard numbers

Question 7

why is it difficult to identifyt the qualitative contributions for growth accounting?

Answer 7

it is tricky since the three factrs comprising the multiplicative term on the cobb douglas production function interact with each others contributions

Question 8

what is the method to disentangle the qualitative contributions for growth accounting?

Answer 8

the first step is to take natural logarithms of the cobb douglas function. ln Y = ln A + b(ln K) + (1-b) ln L. this means the natural logarithm of income is now a weighted sum of the logarithm of technology, capital and labour. you then deduct the last period values of this equation from this years to find the difference. the property that the first difference in the logarithms of variable is a good approximation for this variables growth rate we arrive at change in Y/Y = change in A/A + b(change in K/K) + (1-b)(change in L/L) which is the growth accounting equation

Question 9

what is the growth accounting equation?

Answer 9

change in Y/Y = change in A/A + b(change in K/K) + (1-b)(change in L/L)

Question 10

what is the solow residual?

Answer 10

change in A/A= (change in Y/Y) - b(change in K/K) - (1-b)(change in L/L)
it is an estimate of the rate of growth of technological progress

Question 11

what is the solow growth model?

Answer 11

when the circular flow is in equillbrium, the injections are equal to leakages. assume its a global economy model with no trade or government for simplicity so leakages are zero when I = S. the savings is given by S=sY where s is marginal propensity to save and Y is income. Investment must also equal I=sY. using the production function for Y leaves I =s F(K,L). investment is also an addition to capital where the change in K = I - w(K) where w is the rate of deprecition. this leaves the change in capital = s F(K,L) - w(K). this tell us capital stock grows when the private savings or gross investment exceeds the amount of capital we lose in depreciation.

Question 12

what is the requirement line?

Answer 12

it shows the amount of investment required to keep the capital stock at the indicated level

Question 13

what is a steady-state income?

Answer 13

it is the one level of potential income that obtains once the capital stock has built up to the desired level

Question 14

what is potential income?

Answer 14

it is a short to medium run concept. the capital stock cannot change that much and may as well be taken as given. booms and recessions occur as vertical fluctuations around the potential output level marked by the partial production function

Question 15

why does the capital always end in the steady state income?

Answer 15

if K intially exceeeds K* then the actual investment falls short of the investment level required to replace capital lost through depreciation. so to the right of K* the capital stock must be falling and will continue to do so until it reaches K. if K initially exceeds K then the actual investment will be greater then the required investment and so the capital stock must be rising and will continue until it reaches K* level. once it reaches the steady state capital stock then you can easily read the steady state income of the curve.

Question 16

what is the effect of an increase in the labour force on the solow model?

Answer 16

this will cause the solow growth model to have a partial production function which is steeper and higher for all capital stocks. an increase in the labour force due to higher population will turn the partial production function upwards. this will also cause the savings function to move upwards aswell as if more is being produced at each level of production then more is being saved and invested. since depreciation is independent from population levels, the new investment curve intersects the requirement line a higher level of capital stock . this means that a high population country should also have high capital stocks and high aggregate output (although this says nothing about the income per capita)

Question 17

what is the effect of technological progress on the solow growth model?

Answer 17

the effects of a once only imporvement in technology means that for any given quantity of capital with a given quantity of labour, it yields more output then with the previous technology. therefore the partial production function turns upwards becoming steeper and taller than the previous technology function. the investment function will also turn up aswell since more production means more is being saved and therefore invested. this means that both equilibrium capital stock and output will rise. this will also cause income per capita to rise unlike the effect of a population increase

Question 18

what is the effect of an increase in the savings rate on the solow growth model?

Answer 18

an increase in the savings rate does not have an affect on the production function or the depreciation rate of capital however it will increase the savings function. this means the savings function and the requirement line will intersect at a higher point so the equilibrium quantity of capital and output will be higher. this result means that for a given population and technology, the steady state level of income can be raised by saving more.

Question 19

what is the issue with only considering savings and income relationship?

Answer 19

income is not the main aim but instead consumers aim to maximise the utility they gain from consumption. if all the income is being saved then you will receive little utility. although income may be greater when savings rate is higher they may not gain in utility

Question 20

what is the golden rule of capitla accumulation?

Answer 20

the golden rule of capital accumulation defines the savings rate that maximises consumption. at the resulting capital stock, additional capital exactly generates enough output gains to cover the incurred additional depreciation.

Question 21

what are the steps to pick out the golden steady state from all available steady states?

Answer 21

1. draw in the production function. ignore the savings function for now as we do not know the golden savings rate yet
2. draw in the requirement line. in a steady state actual investment equals required investment. so the requirement line defines all possible steady states available at various savings rates
3. note that the vertical distance between production function and the requirement line measures consumption available at different steady states
4. consumption is maximised where a line parallel to the requirement line just touches the production function. this point defines golden rule output and the golden rule capital stock
5. since the actual savings curve must intersect the requirement line at the golden rule capital stock, this identifies the golden rule savings rate

Question 22

if the actual savings rate is too low compared to the savings rate recommended by the golden rule, should the government interevene through tax incentives?

Answer 22

if the savings rate is too low, then steady state capital stock obtains an accompying consumption that falls short of the optimal consumption. to put the economy back on track then the savings rate will need to be increased. this will succeed in increasing incomes in the long run however in the short run there will be an immediate decrease in consumption at current income. higher savings rate leads to greater capital accumulation and growing incomes which will recover the loss in consumption and eventually it will surpass the original level. the issue is then that consumption in the distant future can only be raised at the cost of the present. the question then is how much weight do we put on the future generations in comparison to present consumption. if future benefits are heavily discounted compared to current costs then it may not be irrational to not raise the savings rate. we call the steady state capital stock that falls short of the golden one dynamically efficient

Question 23

if the actual savings rate is higher then that recommended by the golden rule, should the government try to move it by offering tax incentives?

Answer 23

assume the savings rate is too high which led to a steady state capital stock and a level of consumption that falls short of maximising the steady state consumption. when citizens change their behaviour lowering the savings rate the consumption will rise immediately. however the consumption will gradually fall as the capital stocks begin to be melted away be depreciation however it will always be higher then the initial consumption before decrease in savings rate. this means that to reduce the savings rate will provide individuals with higher consumption today and during all future periods at no cost. not to accept this opportunity to reap this costless gain would be irrational and inefficient so this is why when the savings rate is too high, the steady state capital stock is called dynamically inefficient.

Question 24

what is the intensive form of the production function?

Answer 24

y = f (k) where y is income per capita and k is capital per capita

Question 25

what are the three reasons for capital per capita to change?

Answer 25

1. any investment per capita i directly adds to the capital per worker
2. any depreciation eats away at a constant fraction of capital per worker
3. new entrants into the workforce require capital to be spread over more workers hence capital per worker falls in proportion to the population growth rate n

Question 26

what is the equation for the change in the capital stock per worker?

Answer 26

change in k = i - (a+n)k where n is the population growth rate, i is investment per capita and a(k) is the depreciation of capital per capita

Question 27

what is the components of the slope of the requirement line for per capita ?

Answer 27

capital lost through depreciation per capita and the new entrants into the workforce

Question 28

what is the effect of popualtio growth on capital stocks and income per capita

Answer 28

countries with a higher population growth tend to have lower capital stocks per capita and lower per capita incomes
this is because the higher growth rate will shift up the requirement line meaning the requirement line and the savings function will intersect at a lower capital and output per capita

Question 29

what is unrealistic about the production function and how can we alter the production function toa account for this?

Answer 29

one unrealistic assumption is that the economy in question operates with the saeem production technology all the time. in reality, technology appears to improve continuously. one way to incorporate technology into the production function is by assuming that it determines the efficiency E of labour so the production function then reads Y = F (K, E x L) where ExL is the labour measured in efficiency units

Question 30

what is the formula for the requirement line that tells us how much investment per efficiency unit of labour we need to keep the capital stock per efficiency unit at the current level?

Answer 30

in order to acheive this we need to replace the capital lost through depreciation, cater to new workers and equip new efficiency units of labour created by technological progress which we assume to proceed at the rate e.
therefore the formula is change in k(efficiency terms) = i(efficiency terms) - (a + n + e)k(efficiency terms)

Question 31

what is the effect of faster technological progress on the solow model?

Answer 31

a faster rate of technological progress turns the requirement curve upwards thus lowering capital and income per efficiency unit. this is not necessarily bad however with regard to per capita income as the one of increase in technology raises capital and output per worker. so this means that faster technological progress raises the level and growth rate of output per worker

Question 32

how much affect does the combined influence of investment rates and population have on income per capita?

Answer 32

they find that 60% of the income differences can be traced back to differences in investment rates and population per capita incomes

Question 33

what is the absolute convergence hypothesis?

Answer 33

it states that there is a negative relationship between a countries initial level of income and subsequent income growth. those countries with low capital stock will grow at a faster rate then those with a high capital stock and as a result catch up. it is only true for countries with the same steady state that is with similar investment rates and population growth.

Question 34

what are the important questions that the solow model does not answer?

Answer 34

some 40% international differences in per capita incomes cannot be attributed to differences in population growth and investment rates as the workhorse model indicated. this suggests that not all countries operate on the same partial production function(we might have overlooked a important production factor)
from global perspective there seems to be no convergence of income levels. this can partly be attributed to differences in population growth and investment rates but might also mean view of production function is too simple
it does not explain economic growth but rather says per capita occurs driven by exogenous technological progress as a residual which the model does not attempt to understand

Question 35

what is the only factor that in the presence of constant returns to scale can make living standards grow?

Answer 35

in the long run only technological progress can raise living standards in the presence of constant returns to scale