ECONOMICS OF GROWTH AND DEVELOPMENT
IGNOU MEC 04 Solved Free Assignment
MEC 04 Solved Free Assignment July 2023 & January 2024
Q. 1. Examine the effect of population growth in the Solow model of economic growth. Discuss how the Solow model could be used to explain poverty traps in developing nations.
Ans. Population is an asset as well as a liability. Solowian model is also used to explain the effect of increase in population on growth rate.
If in an economy, population is increasing, at a rate denoted by n, it will increase the number of workers available and hence, capital per worker i.e. k will fall. We know that
Ak=sf(k) - nk
So, an increase in population (n, the level, not rate) reduces k.
Now if there is change in the rate of population itself, say, population increases from n, to n,, then n line will tilt upwards. New equilibrium will be at to the left of previous equilibrium point.
This will cause k to fall. As it has been explained earlier, y f(k), a reduction in k will reduce y as well. IGNOU MEC 04 Solved Free Assignment 2023-24
Therefore, a developing country must take care that population does not increase too much in order to maintain full employment equilibrium.
Solow Model claims that over a long period of time, all nations of the world would tend to converge towards same rate of growth. It is referred to as convergence.
Following reasons are given for convergence:
(a) Since rate of return on capital is higher in countries where capital is relatively scarcer, hence, capital will flow from the developed countries to developing and under-developed countries.
(b) As Solow model claims that all countries attain balanced growth path in the long run, it would converge.IGNOU MEC 04 Solved Free Assignment 2023-24
(c) As capital will move from developed countries to developing and under-developed countries, the incomes of poorer countries will also increase.
Types of Convergence
(a) Absolute Convergence: It states that if n number of countries have access to same technology, have same saving ratio, same population growth rate but different capital output ratio, then all countries would converge to same level of equilibrium steady growth rate.
It is so because capital output ratio will be higher in poor country and hence, capital and output in poor country will grow at a rate faster than the rate of growth of population.
While, capital and output in rich country will grow at a rate slower than the rate of growth of population. It implies that the poor country will grow at a faster rate than rich country. The gap between two counties will narrow down.
Empirical evidence has not supported the existence of absolute convergence. So, the concept of conditional convergence came into the picture.
(b) Conditional Convergence: Conditional convergence states that if n number of countries has access to same technology, same population growth rate but different saving ratios and capital labour ratio, then there will still be convergence at same growth rate but equilibrium capital-output may or may not be equal.
This is so because of paradox of savings which states that a permanent change in savings rate i.e. MPC has only temporary effect on the economy’s growth rate.
In real life scenario, even conditional convergence is not observed because different countries have different population growth rates.
In order to examine the validity of the unconditional convergence, a well known study was conducted by Baumol, which should have shown inverse relationship between initial per capita level and growth rate of per capita income to prove that conditional convergence actually operates.
But, Baumol found a regression which showed almost perfect convergence. Baumol’s findings were challenged by Bradford De Long on two grounds: (a) Sample selection was biased; (b) there was measurement error in the findings.
Neo-classical model exclaimed that in the long run, all nations of the world would tend to converge towards same rate of growth. But the hypothesis did not hold true in real scenario. IGNOU MEC 04 Solved Free Assignment 2023-24
This was claimed that poor nations will grow at a higher rate and gradually the gap between nations will disappear.
But the poor nations were actually caught up in a situation where they could not come out of the vicious circle of poverty. This is called poverty traps. Poverty traps can be
(a) Technology induced;
(b) Population induced.
(a) Technological Trap: Technological trap states that if a country receives an initial injection of capital so as to increase k, the level of output will be pushed over.
It is called ‘Big Push Theory’. Poverty trap is caused by low savings, backward technology and is also called vicious circle of poverty.
(b) Population Trap: Neo-Classical Model assumes that population is a factor which is exogenously determined at a rate denoted by n. but as is explained by demographic theory of population, that with increase in standards of living birth rate continues to be same, but death rate fall in second phase leading to population explosion.
Now if population growth is not exogenously determined by is a function of per capita income y, then
Y=F (K/L) n = F (K/L)
If there is a given range of k say k, -k, then for kk,, n is <0. For any value of k between k, and k,, n is >0. When n is > 0, the value of n itself ƒ can change. It will lead to change in shape of saving curve and may not be S shaped any more.
In this situation, it can intersect sf(k) at many points and we may have multiple equilibrium points of k, which are unstable and hence there is instability in the economy. That value of k will give s stable equilibrium which lies within our range of k, – k
Q. 2. Describe the Mankiw-Romer-Weil extension to the neoclassical model to include human cpital. Explain why diminishing returns to capital do not take place in the AK model.
Ans. After understanding the implications for economic growth, of expanding the notion of capital to include human capital, the effects of human capital on economic growth were explained. IGNOU MEC 04 Solved Free Assignment 2023-24
Now let us discuss the nature of human capital and the way it is created. No doubt, human capital will aid the growth process. But the model will help us to quantify the relation between growth and human capital.
Let us look at a standard Cobb-Douglas production function in the human capital augmented neo-classical- growth model. y = Aet Ka L1-a
In such a model, savings will create growth for a while but it will not be steady and sustaining growth.
As the ratio of labour to capital would rise, marginal product of capital will fall and the economy would revert back to the same level of growth.
Growth in income per worker will continue to take place and grow and which is an indicator of increase in the level of human capital.
Traditional neo-classical theory takes m as an exogenous variable but endogenous growth theory explains how is the value of n determined.
AK Model of Endogenous Growth: AK model of endogenous growth was presented by Sergio Rebelo through his article titled ‘Long Run Policy Analysis and Long Run Growth’ which was published in 1991.
It is based on the work done by Romer and Lucas. The basic equation of the model is:
Y=AKIGNOU MEC 04 Solved Free Assignment 2023-24
Where A is symbolic of factors affecting technology and K includes physical as well as human capital.
The model rejects that proposition of diminishing returns. It claims that externalities or spillovers and increasing quality and variety of intermediate inputs do help to avoid diminishing returns.
Therefore, growth rate of output is equal to growth rate of investment. Generally speaking, lesser importance has been given to technology because endogenous growth theory admits that technology does not explain much of the growth.
Initially technology was given a high importance. But then some economists claimed that there is not much need to understand technology as it is a very small part of the contribution to growth process.
They feel that it is so small that it can even be ignored. But it is not logical. Solow model as well as empirical evidence shows that even if capital formation directly contributes to growth, without technological advancement, growth would stop.
It is so because it is technology that causes investment in the capital and indirectly causes all the growth. IGNOU MEC 04 Solved Free Assignment 2023-24
It is technological advancement that makes it possible to get increasing returns from all relevant inputs.
Technology connotes the way in which inputs are converted into output. Technology can be taken as a factor which stimulates the productivity of all factors of production.
In a Cobb-Douglas production function, technology can be shown as: Y = Ka (AL)1-“, where A is an index of technology.
Paul Romer’s views on technology and its impact on growth process:
Romer published his two papers in the year 1986 and 1990 in which he presented a way of modeling ideas as an engine of growth. Romer claimed that new ideas are non-rivalrous good and hence produce increasing returns to scale.
He further claimed that increasing returns to scale with explicit presence of research can prevail if and only if there is imperfect competition in the market.
Most of the economic goods are non rivalrous in nature. This means that if good X is used by someone, everyone else is excluded from using same good X. unlike economic goods, ideas are non rivalrous in nature.
Once an idea is created, it is available for all. But ideas can be excludable particularly if they carry copyrights or patent rights.
In such cases, the creator of the ideas can charge a price for their ideas. Goods that are excludable benefit their producers in the form of higher incomes.
Goods that are non-excludable benefit the whole economy by producing externalities and spill overs.IGNOU MEC 04 Solved Free Assignment 2023-24
Rivalrous goods need to be produced as many times as it is consumed. If say a book is sold once, we need to produce another book for next customer.
But non excludable goods can be consumed by unlimited number of people once they are produced. Say for example, a road, it can be used by thousands of people in one day but do not have to be created again and again.
It implies that non excludable goods have a fixed cost and zero marginal cost. It takes effort to create them in first go and then it can be used many times.
Such cost structure implies increasing returns to scale and imperfect competition. The cost of knowledge capital is fixed and subsequent units can be produced under constant returns to scale.
Since, the units after the first unit are getting produced under constant returns to scale then the entire production takes place at increasing returns to scale therefore, AC curve is downward sloping.
Therefore, we have understood following facts:
(a) Ideas are non-rivalrous in nature;
(b) They produce increasing returns to scale;
(c) Non-rivalrous goods have a fixed cost of production and zero marginal cost. It applies to ideas as well.
It implies that if we attain producer equilibrium by equalizing MR and MC, price will always be less than AC and thus losses.
When someone produces a useful idea, he is given a patent or a copyright on the same if he applies for it. It gives him monopoly powers and he is able to reap profits from their ideas and inventions.
Perfect competition would not sustain time dependent production functions for technical change because the firms would operate at a minimum efficiency level and it is not beneficial to increase the size of the firm.
Romer’s Model of Endogenous Technological Change: Romer assumed production function to be equivalent to: Y = Ka (AL)1-a where L is labour; A is stock of ideas; a lies between 0 and 1; K is capital. IGNOU MEC 04 Solved Free Assignment 2023-24
If L and K are doubled, then output will double. If L, K and A is doubled then output will be more than doubled. Hence, A causes increasing returns to scale.
In Romer’s model, capital accumulates as people save at a constant rate and it is similar to that of Solow model. There is also depreciation of capital.
Labour grows at a constant rate n. Romer introduced an equation that describes the accumulation of ideas. In the neo- classical model, A is the productivity term and increases exogenously at a constant rate.
But in Romer’s model the growth of A is taken as endogenous. Given the stock of knowledge accumulated till a time period t, At = dA/dt is the number of new ideas produced.
In Romer’s model if a particular fraction of the population is engaged in production of ideas i.e. R and D, then the model predicts that all growth is due to technological progress. IGNOU MEC 04 Solved Free Assignment 2023-24
Rate of growth of output will be equal to rate of capital formation and rate of technical progress. Along the balanced growth path, A will grow at a constant rate.
There are three sectors in Romer’s model:
(a) A Final Goods Sector;
(b) An Intermediate Goods Sector;
(c) Research and Development Sector.
In the economy, the R and D sector produces ideas, and sells the right to use these ideas to intermediate sector which in turn uses these ideas to produce capital goods.
These capital goods are sold to final goods sector which produces consumer goods from it.
The intermediate sector is monopolist and there is imperfection in this sector.
Introduction of monopolistic competition has made us realize that firms spend on creating ideas, earn monopoly rights on them; and then charge monopoly rents for them.
The basic equation of the model is:
Y = AK
Where A is symbolic of factors affecting technology and K includes physical as well as human capital. The model rejects that proposition of diminishing returns.
It claims that externalities or spillovers and increasing quality and variety of intermediate inputs do help to avoid diminishing returns.
Generally, speaking lesser importance has been given to technology because endogenous growth theory admits that technology does not explain much of the growth. Initially, technology was given a high importance.
But then some economists claimed that there is not much need to understand technology as it is a very small part of the contribution to growth process.
They feel that it is so small that it can even be ignored. But it is not logical. Solow model as well as empirical evidence shows that even if capital formation directly contributes to growth, without technological advancement, growth would stop.
It is so because it is technology that causes investment in the capital and indirectly causes all the growth. It is technological advancement that makes it possible to get increasing returns from all relevant inputs.
Q. 3. Distinguish between economic growth and development. Briefly mention the main benefits that economic growth confers upon society.
Ans. The difference between economic growth and economic development are:
Economic Growth is quantitative while economic development is qualitative.
Economic growth is comparatively a narrow concept and development is much more comprehensive. IGNOU MEC 04 Solved Free Assignment 2023-24
Economic growth refers to increase in the total output of final goods and services in a country over a long period of time.
In contrast, economic development refers to progressive change in the socio-economic structure of the country. It includes gender equality, change in composition of output, shift of labour force from agriculture to other sectors.
Economic growth is easy to realize as only monetary aspect is involved. But, it is very difficult to attain the goal of development as it involves many socio-economic-political aspects.
Economic growth can easily be estimated by real GDP or Real Per Capita income. But it is very difficult to measure development as it has some aspects that can’t be quantified. Economic development however is indicated by Human Development Index.
Economic growth can take place without Economic development; however, economic development can’t take place without economic growth.
There is no empirical evidence to the fact that there is a strong and positive relationship between wealth resulting from rapid growth and happiness.
To your surprise there is evidence of high levels of dissatisfaction in the high income countries than low income countries. But don’t misinterpret the fact that growth is undesirable. Certainly it is not. IGNOU MEC 04 Solved Free Assignment 2023-24
Economic growth can alter the relative incomes compared to other economies. There are many advantages of having a high economic growth rate.
Some of these are listed below:
It creates ability to access better standards of living in materialistic terms. It allows people to expand their consumption pattern from only basic to education, health, scientific research, entertainment, tourism etc.
An economy where national income is too low, people can’t afford even the basic needs how can we think of expanding effective demand.
Higher rates of economic growth means higher level of per capita income which lead to reduction in social conflicts arising for housing, better wages, health, education and other amenities.
When resources are abundant, there are lesser conflicts which in turn reduces crime rate in the country.
Higher level of economic growth might help human beings to have a better control over environment. It might help to increase life expectancy, getting cure for many diseases and expanding control over resources.
Economic growth always tends to increase the number of women involved in economic activities. IGNOU MEC 04 Solved Free Assignment 2023-24
It helps them to have a better control on their lives, improves their value in the family and certainly enhances labour force for the economy which helps in further enhancement of the rate of economic growth.
Reduction in gender inequality also solves many other social issues relevant for economic development like infanticide or adverse sex ratio.
Economic growth can help a society to come out of many problems which arise due to financial crisis. It is very much possible that as income rises, some people might get willing to forgo a part of their income to uplift the needy.
Poverty alleviation can best be done through higher rates of economic growth in an economy. This is called trickle down effect.
As an economy grows, the benefit of growth trickles down to all sections of society and hence gradually poverty gets alleviated.
Q. 4. Describe Pasinetti’s theory of economic growth and distribution.
Ans. Pasinetti’s theory of growth and distribution is a refinement or a corrected reformulation of Kadlor’s model.
He criticized Kadlor’s model for its formulation of existence of only one saving ratio that keeps system in equilibrium for any given rate of population growth and technical progress. IGNOU MEC 04 Solved Free Assignment 2023-24
In his words, “In any type of society, when any individual saves part of the income, he must also be allowed to own it; otherwise he would not save at all.”
Accordingly, he divided total profits into two parts one part accrues to the capitalists and other to the workers.
Reformulating the Kaldorian Model
As given above, he catagorised profits into two parts, so-
Where, P and P, stand for the respective share of capitalists and workers in the profits.
Therefore, new saving functions are S,,S,(W+P) and SS.P and equilibrium condition is om
I=S1 = S (W+P1) and Sk = Sk
From this we can derive the following general equations. These two equations contain all the elements required to correct the post Keynesian theory of income distribution.
P/Y=1/S-S. I/Y – S/S – S + I (SS/S – Sw.. K/I-S/S – SK/Y)
Rate and Share of Profits in Relation to the Rate of Growth
Pasinetti maintains that in the long run model, rate of interest must be equal to rate of profits. In such a case one can substitute P/K for I, and we get:
P/K (S (I-SY) A
Hence, the result is that we do not need to make any assumptions about propensities to save of the workers.
In the long run, MPS of workers influences the distribution of income between workers and entrepreneurs but does not influence the distribution between profits and wages and the rate of profits.
Fundamental Relation between Profits and Savings
Pasinetti proved that in the long run profits will be distributed in proportion to the amount of savings that are contributed by workers and entrepreneurs respectively.
No matter how many categories of economic agents are there, the ratio of profits to savings will always be for all categories.
Implications of the Model
Two conclusions given by the model are:
- As the model gave conclusion without assuming a constant saving ratio, it has become much wider. The model does not demand to take any hypothesis about saving behaviour of the workers.
- The relation between capitalists’ savings and capital accumulation is based on simplifying and drastic assumption of negligible savings by the workers.
Conditions of Stability
- Prices are flexible with respect to wages.
- Full employment investments are carried out.
Q. 5. Describe the various approaches to the measurement of total factor productivity.
Ans. There are five methods of measuring total factor productivity. The first two are growth accounting techniques and the other three are econometric tools.
Data Envelopment Analysis (DEA): This approach to productivity measurement is completely non-parametric and makes use of linear programming.
This technique was first used by Farrell in 1957 and later it was operationalised by Charnes, cooper and Rhodes in 1978. This approach compares the ratio of linear combinations of outputs over linear combinations of inputs.
It defines that a firm is efficient which has highest output-input ratio for any combination of outputs and inputs. In some situation no firm may be efficient.
Index Numbers (TFP): In this approach, under a number of assumptions, it is possible to calculate A, the technology coefficient or TFP coefficient without a specified exact production function or rigidly assuming it to be uniform across observations.
There are two indices: Solow Index (developed by Solow in 1957) and Translog index (developed by Diewert in 1976).
Solow Index: Solow index assumes that elasticity of substitution between labour and capital to be equal to one. IGNOU MEC 04 Solved Free Assignment 2023-24
In other words if interest goes up by 5% employment of labour will increase by 5%, it has an important implication that income shares of labour and capital remain constant. Solow index of TFP is equal to:
InA = InY -(1-α)InL – alnK
Translog Index: The translog index of TFP is equal to:
AlnTFP, AlnY, -[(SL, + SL, -1)/2* AlnL,]
- [[(SK, +SK, -1)/2 * AlnK,]
Where, Y is output, L and K are labour and capital respectively, SL and SK are shares of income of labour and capital respectively, TFP is total factor productivity.
Advantages of this index:
- It does not take rigid assumptions about elasticity of substitution.
- It does not require technology progress to be Hicks neutral.
- Specification of technology is flexible.
- Method can easily handle multiple outputs and a large number of inputs.
Disadvantages of the index:
- It requires quality and reliable data.
- It is impossible to account for measurement error.
Econometric methods: In econometrics, we apply regression analysis to estimate a production function and from estimated production function we get the rate of technical progress.
Generally, Cobb-Douglas Production function is used. There are also Semi parametric procedures to address the issue of productivity.
Limitations of Total Factor Productivity Measures
(a) Certain rigid assumptions make it unrealistic and hence limit its use in real life.
(b) Econometric models do not take such rigid assumption and hence are appreciated but it assumes that same rate of technological progress for all the years under study. It is not so.
Q. 6. What are the main propositions of the Real Business Cycle model? Describe the basic structure of a prototype Real Business Cycle model.
Ans. Real Business Cycle model is technically an explanation of Brock-Mirman Model. They explained, “What happens under uncertainty” and Real Business Cycle explains, “Why does it happen so?”. It tried to explain the reasons for fluctuations in economic activity at macro level.
Real Business Cycle model Makes two types of propositions:
(a) It says that long-term growth and short-term fluctuations in economic activity are studied separately but for both of them same reasons are responsible.
The theory uses the word fluctuations and not cycles as the latter conveys as if it occurs regularly which might not be true.
(b) The word ‘real’ in the Real Business Cycle Model suggests that this theory like classical economists considers money to be veil and plays down the role of monetary forces. IGNOU MEC 04 Solved Free Assignment 2023-24
In their opinion money plays a neutral role and fluctuations are brought about by real factors like investment, demand, supply etc.
The Real Business Cycle Model criticizes on Keynesian approach that it gives too much emphasis on the aggregate demand.
This theory gives a greater emphasis on supply side and therefore, is sometimes also called ‘New-Classical’.
However, there can be many types of external shocks. These shocks can originate on either demand side or supply side.
These shocks may be caused even by monetary and fiscal policy of the government. But the focus of The Real Business Cycle Model is on productivity shocks.
There are different types of productivity shocks:
(a) Development of new techniques;
(b) New management practices;
(c) Bumper crop or crop failure;
(d) New Suppliers coming from external economy etc.
The Real Business Cycle Model explains productivity shocks and the extension as well as impact of these shocks on other variables in the economy.
The Real Business Cycle Model is built upon Brock-Mirman Model of the type in which discounting is present. The model explains a decision regarding labour and leisure where it is assumed that leisure also gives utility.
The structure of the model is similar to that of optimization under uncertainty.
We need to maximize a utility function like Ea’u(c,+j,l, ‚+Jil+D)].
Here c and I are household’s and leisure activities.
Each household has access to a gives technology (as each household is playing dual role in the economy. Each hosuehold is a firm as well.
Y1 == (L,K)
When Z=randorm verible depicting technology L and K denote lobous and capital supplied in the time period 1. L=1 / where / is leisure
therefore, the Budget constraint is:
c+KZ,f (L,K) + (1-8) K, -w (LL)-r(KK)
Where w wage rate
r = rate of interest
This equation is explained one should usury dynamic programming and a constrained optimization increase. It also explains shocks how they generated in the economy.IGNOU MEC 04 Solved Free Assignment 2023-24
Q. 7. Compare and contrast the Uzawa two-sector growth model with the Feldman model.
Ans. Uzawa’s two-sector growth model considers a Solow Swan model with two produced commodities, a consumer good and an investment good. Both these goods are produced with capital and labor.
So we have two outputs and two inputs, of which the most interesting feature is that one of the outputs is also an input.
To use the old Hucksian analogy, in the Uzawa two-sector model, we are using labor and tractors to make corn and tractors.
For the following exposition, we have benefited particularly from Burmeister and Dobell (1970) and Siglitz and Uzawa (1970).
Let us follow the basic setup of the Uzawa two-sector model. We begin with the following definitions:
Y = output of consumer good
L= labour used in consumer good sector
K = capital used in consumer good sector
Y, output of investment good
p = price of investment good (in terms of consumer good)
L, labour used in investment good sector
K;= capital used in investment good sector
Y = total output of economy
L = total supply of labour
K = total supply of capital
w = return to labour (wages)
r = return to capital (profit/interest).
The principal equations of the two-sector model can thus be set out as follows:
Ye=Fe(Kes Le) consumer sector production function
Y, F,(K,, L)
Y=YpY, Le + Li-L
K2+K; = K
investment sector production function
- labour market equilibrium
- capital market equilibrium
p'(dY/dL)- labour market prices
r=dYJdK= p(dY/dK) – capital market prices
- labour supply growth – capital supply grow
These equations should be self-evident. The consumer goods sector and the investment goods sector each use both capital and labour to produce their output.
We capture this with equations (1) and (2), where F, is the consumer goods industry production function and F, the investment goods industry production function.
Both production functions F, and F, are nicely neoclassical, in the sense of exhibiting constant returns to scale, continuous technical substitution, diminishing marginal productivities to the factors, etc.
Equation (3) is merely the definition of aggregate output, expressed in terms of the consumer good. Equations (4) and (5) are also self-evident: the market demand for labor is L. + L, and the market demand for capital is K. + K1.
As L and K are the respective supplies, then (4) and (5) are merely the factor markets equilibrium conditions so that demand equals supply in each market.
There are differences in the basic assumptions on which both the models have been constructed. Therefore there is also a difference between their outcomes and implications. Following are the differences in the assumptions of the two models:
1.Uzawa model assumes that there is one single capital good which is used in both the sectors as an input. Say for example, the economy produces ‘Corn’ in one sector using tractors and labour and ‘tractors’ in other sector using tractors and labour.
However, the Feldman model assumes that the economy is divided into two sectors such that sector A produces capital goods and these capital goods can be used in either sector but once installed they can’t be shifted form one sector to another.
The Feldman model assumes that production is carried out in both the sectors with fixed coefficients technology and Uzawa assumed that labour and capital are shiftable from one sector to anther without any cost as such and instantaneously.
Uzawa model assumes that physical capital depreciates at a constant exponential rate 8. The Fredman Model claims that capital does not depreciate at all and hence capital is equal to investment.
The Fredman model also assumes that the economy is a closed economy however; Uzawa model is silent on it.
The Fredman model takes another assumption that production of goods in sector 1 is independent of production of goods in sector 2.