A little development economics

Transcription

1 A little development economics Halvor Mehlum, January 29, Background Many results in economics builds on the premise of diminishing returns in production In terms of employment diminishing returns implies that if hours worked is doubled the production is less than doubled If hours worked is very high at the outset, an additional hour may even reduce production One illustration is given in Figure 3, where is hours worked and Y is the value of production To the left of Y increases as hours worked increases, but at a declining rate To the right of further increases in actually lowers production Y In some contexts diminishing returns may be an accurate description in other cases not Diminishing returns, or diminishing marginal product, may for example be a reasonable assumption on a farm with a limited stock of capital and land In the following I will show some important results based on the premise that the marginal product of labour is indeed decreasing I will use an example where the return to employment declines following a linear formula I could have illustrated all the following qualitative results using any formula for diminishing return I choose to use the linear example because it is simple 2 Marginal product The value of the marginal product x captures the contribution to the value of production by the last of the hours worked Total production Y is then the sum of x for the first, second, third, th hour In Figure 1 the marginal product x is given by a linear relationship x is the marginal product, is total hours worked by all workers, a and b are constants [Example: a = 10, b = 1] x = a b (1) 1

2 Figure 1: Value of marginal (and average) productivity value x x x starts out in a and has a negative slope of b All employees are assumed equal but the first hour worked is quite productive while the next is less and so on until where further employment is unproductive 1 Given the formula above the maximum productive employment is found by setting x equal to zero and solving for as follows x = 0 = a b = a/b [Example: = 10/1 = 10] Before deriving the value of production Y it is convenient to find the value of the average product x It tells us what is produced during each hour on average The average product, x, is the average of each of the marginal products In the linear case the average product is the average of the x for the first hour worked and the last hour worked Think of as a large number, say 2000, then the marginal product for the first hour worked is approximately equal to a while the marginal product for the last hour worked is equal to (a b ) The average of these is x = a + (a b ) 2 = a b 2 x starts out in the same point as x but is less steep and crosses the horizontal axis at 2 Now it is easy to find the value of total production The value of total production Y is the sum of all the marginal products for all hours worked Therefore Y is equal to the area between the x curve and the horizontal axis An expression for Y is found from the fact that total production is also equal to the average product times the number of hours worked Y = x = (a b2 ) = a b 2 2 (2) In Figure 2 these relationships between Y and x and x are illustrated In the left panel Y is found as the area under the x curve (a sum of narrow columns one column for each hour worked) In the right panel Y is derived as x The two diagrams illustrates total 1 For example as workers are obstructing each other as in a soft ice kiosk with 30 workers 2

3 Figure 2: Total production Y as two areas value ˆ x area under the marginal product value ˆ x average product times hours worked ˆ Figure 3: Total production Y ˆ production Y when = ˆ When =, Y reaches it s maximum If is increased further the x goes negative and there is negative contribution to production In the right panel, if is increased beyond the rectangle gets wider but less tall In fact any to the right of gives a smaller rectangle = is the amount of employment that gives the highest production Y The value of production Y as a function of employment (see (2)) is given in Figure 3 Knowing the relationship between the value of production Y, the average product x and the marginal product x we can investigate a number of important topics 3 The tragedy of the commons Consider a completely isolated village with lots of people/labour and where the only production process available satisfies the function given by (1) For concreteness assume that the production in question is fisheries in a closed pond with some reproduction One fisherman will get a lot of fish, two will get more (but not double), and so on Maximum catch is reached with fishermen If exceeds there will be overfishing and the total catch will start to decline Assume first that all decisions are taken by a village council Their aim is to get the maximum production in the village and to distribute it evenly between all the 3

4 villagers How many workers should be employed in order to get the maximum production? The answer is simple The council should employ people until and share the production between all the people (if there are too many workers the solution may be that each worker works half time) Assume now that the council is closed down et each person in the village cater for themselves and assume that no one owns the pond It is a common property ie commons In that case each and every fisherman will, depending on the total number of fishermen, get the income x The result will be that every of the persons start as a fisherman As >, there will be too many fishermen Note that if the number of people in village is very high ( ) > 2 the outcome will be total extinction of the fish The number of fishermen will grow until 2 and at that point there is no more fish The tragedy of commons problem is that when production involves a common property with free access, there will generally be over utilization of the common property The reason is that each individual entering gets the average product x which by definition is larger than the marginal product x Another way to put it is that each individual do not take into account that him entering lowers the return to all the others who has already entered There is an externality, there are wrong incentives Note that the tragedy is that there is no regulation of the utilization of the pond It is perfectly possible to get optimal harvesting of a common property if the use is regulated by a village council 4 Alternative employment The discussion above was based on the assumption that there was no alternative employment Assume now that the villagers can travel to the neighboring village and work in a factory for a fixed wage w In the case of a council, with the interest of all the villagers as their priority, the council will decide that a number of workers A stay in the village and require that the remaining fraction ( ) A of the workers work in the factory for the wage w Again, the council wants to maximize total income: the sum of what is earned in the neighbouring village (w ( ) A ) and what is produced Y As long as w > x income increases as workers are moved from fishng in the pond to the factory As long as w < x income increases if workers are moved out of the factory and to fishing in the pond Maximum income is reached when w = x that is, when the wage in the factory is equal to marginal product in the village The optimal allocation of labour is illustrated in Figure 4, where the shaded area captures total village income If A was moved to left or to the right either of the two dark triangles would be lost and income wold drop, hence A is the optimum A village council would realize 4

5 Figure 4: Optimal allocation of labour value A x w this and distribute the labour such that A worked in the village and A worked in the factory Eventually all income could be shared equally 5 Private ownership The description above could also capture the production in a private firm selling ice cream in a park The first worker will have a lot of sales, two will sell more but will not be able to double the sales and so on - decreasing returns We can further assume that the owner of the firm hires labour for a fixed wage w Now, the owner wants to hire workers in order to maximize his profits π et us call the choice of workers B His profits is given by the value of production Y minus the wages paid w B π = Y w B As long as w < x profit increases when the owner hires more workers As long as w > x profit increases if workers are sacked Maximum profit is reached when w = x The optimal hiring of labour is illustrated in Figure 5 In the upper panel the profits π are drawn In the lower the profits are equal to the area between the x line and the w-line The optimum is B If is moved to left or to the right of B the net loss would be either of the two dark triangles and profits would drop, hence B is the optimum from the owners point of view 5

6 Figure 5: Profit maximizing owner profits B value B x w This diagram also shows that under these assumptions profits and employment are negatively affected by an increase in the wage Hence, a wage increase will imply that some workers are fired Whether the workers on average are better or worse of is an open question In classical growth theory (Ricardo, Marx and others) the size of profits determines investments and hence how the x moves to the right over time If profits are high x will move a lot to the right It follows that low wages in one period generates high profits that in turn generates high demand for labor (x far to the right) in the next period Wage moderation may therefore benefit the workers in the long run as the firms expand In a globalized world high profits may attract foreign investments leading to a similar result However, if in a globalized world investments go to the country with the best profits opportunities, there will be a competition for having the highest profits This may lead to a competition for having the lowest wages This mechanism is a variety of social dumping 6 Sharecropping et us now move to agricultural production Assume that it is not possible for a land owner to monitor how much the farmers/workers actually work Without such monitoring the farmers/workers may go to sleep whenever the land owner looks in another direction If this is the case the land owner may let each farmer have a peace of land that the farmer has total 6

7 Figure 6: Sharecropping value B C x γx w responsibility over The deal is that the farmer keeps a fraction γ of production and gives a fraction (1 γ) of the production to the land owner(for example γ = 50%) Supose that here also in this case factory employment is an option and consider the case where there is only one family of farmers so that is the working hours available from the family members, C is the hours worked on the land, while C is the hours worked in the factory Since the farmers only keep γ of what they produce the incentive to work on the land is limited The family now wants to maximize total income: the sum of what is earned (w ( C ) ) and their share of what is produced γ Y From above you know that the increase in Y by an increase in is given by x It follows that the increase in γy by an increase in is given by γ x As long as w > γ x income increases as workers are moved from the land to the factory Maximum income for the farmer is reached when w = γ x The equilibrium is illustrated in Figure 6 Since the farmers only keep a fraction of what they produce they are less willing to work on the land than in the case where they keep everything C is too low The return to the farmers is the gray area while the return to the land owner (1 γ) x is the dark area the triangle to the right of the dark area is lost 61 and reform One way to have the farmer and the landlords interest to go in the same direction would be to confiscate the landlords land and give it to the farmer After the reform the landlord and farmer is now the same person The land reform has made the farmer into a landlord 7

8 Figure 7: abour market with market clearing wage value x w that is working on his own land When this is the case the farmer get everything that is produced As a result he will work optimally at a level corresponding to B 7 abour market Consider a town where there are a number of privately owned firms that each have a technology with diminishing returns Monitoring of workers is not considered a problem The marginal product of all firms taken together is now x Firms will hire workers until the marginal product is equal to the wage et the number of workers in the town be fixed and equal to If there is free competition the competition for workers will ensure that the wage is equal for all and that supply of labour, is is equal to demand This is illustrated in Figure 7 In this case the wage level w is the outcome of the interaction between supply and demand Unemployment If for some reason the wage is set at a level ŵ above the market clearing wage w, there will be unemployment The level of ŵ may be the outcome of pressure from the labour unions, it may be given by law, or it may be the minimum level required for a reasonably healthy workforce Unemployment is illustrated in Figure 8 The unemployment U is equal to the difference between labour supply and the labour demand (at the fixed wage ŵ) U = ˆ 8

9 Figure 8: abour market with unemployment value ŵ w x U ˆ Note that the expected wage in the town is the probability of getting a job, ˆ/, times the wage expected wage= ˆ ŵ Harris-Todaro(see more below): If the expected wage is high more people may want to move into town The result is that increases and so does U and the expected wage declines This is the mechanism that drives many of the results in Harris-Todaros migration model Malthus: In a stylized version of Malthus view of the world ŵ is determined by reproduction If not all workers earn at least ŵ the population will decline If workers earn more, population will grow Hence the labour supply will adjust over time so that supply of labour always is equal to the demand ˆ at the wage ŵ Investments: As in the analysis of sharecropping, investments in new firms will increase the marginal productivity of labour, x When the wage is fixed at ŵ profits will increase If there is full employment and the wage is flexible, investments wil raise the wage and profits may not go up at all In the first case investments is a good idea In the latter it may not be such a great idea for a capitalist even tough the workers gain a lot 8 Migration If we consider an entire economy the assumption about employment opportunity in a factory at a fixed wage becomes unrealistic If firms are privately owned, the demand for workers from modern firms should behave according to the profit maximizing principles discussed above and the wage will decline with increasing employment 9

10 Figure 9: Allocation of labour between Agriculture and Manufacturing value in $ value in $ x A x M w A M w Consider an economy where there are two sector and where the demand for labor is declining as the wage increases The manufacturing sector (M) employs M workers and has marginal product x M The agricultural sector (A) employs A workers and has marginal product x A Then if there is full employment in the economy (all workers have a job) and if workers move to the sector with the highest wage we have the two conditions x A = x B = w and A + M = The equilibrium in this economy is illustrated in Figure 9 The width of the diagram is determined by, A is measured from left to right while M is measured from right to left The marginal product in $ in agriculture is drawn from left to right while the marginal product in $ in manufacturing is drawn from right to left Note that the wage w is determined by the interaction between a fixed supply and demand from two sectors A and M Note also that this is in effect the Harris-Todaro model of migration in the case where the wage is completely flexible in both sectors If, due to investments, the demand for labor in manufacturing went up, the x M line would shift up and in the new equilibrium workers would have moved from the rural villages and to the town where manufacturing takes place ( M up and A down) Unemployment (Harris-Todaro model) If for some reason the wage in town is set at a level ŵ above the market clearing wage w, there will be unemployment The level of ŵ may 10

11 Figure 10: Harris-Todaro: allocation of labour between Agriculture, Unemployment, and Manufacturing value in $ value in $ x A ŵ xm w AV w A A M U be the outcome of pressure from the labour unions It may be given by law Or it may be the minimum level required for a reasonably healthy, efficient workforce Unemployment is illustrated in Figure 10 The unemployment U in town is equal to the difference between labour supply A and the labour demand M (at the fixed wage ŵ) U = A M The size of U is determined by how many workers that find it worthwhile to hang around in the town even without a job The reason for hanging around is that there is a chance of getting a job in the modern sector at the wage ŵ as long as you stay in town One simple formulation assumes that workers will move to town until the average wage in town (for the M employed and the U unemployed) is equal to secure wage in agriculture w A = x A Assuming for simplicity that the unemployed earns nothing, the average wage in town is w AV = 0 U + ŵ M U + M For a fixed ŵ and M, w AV will be lower the higher is U When U is zero then w AV = ŵ Note that hence, for fixed ŵ and M, the w AV (U + M ) w AV = M ŵ curve will be the collection of all combinations of (U + M ) and w that multiplied together yields the fixed number M ŵ In other words 11

12 it is a hyperbola The equilibrium is found where w AV = w A as illustrated in Figure 10 9 Comparative advantage and international trade An influential theory for international trade goes back to Ricardo and Smith It encompasses the concept of comparative advantage Comparative advantage can be illustrated in the following model Consider an economy with two sectors: The manufacturing sector (M) employs M workers and has marginal product x M and price p M The agricultural sector (A) employs A workers and has marginal product x A and price p A Assume that the marginal product in each sector is decreasing in the employment (diminishing returns) and assume that each sector has optimal level of employment given the wage w This implies that the value of the marginal product in $ (eg x A p A ) is equal to the wage w For both sectors this implies that x A p A = w and x M p M = w Assume also that there is full employment so that A + M = where is the total labour supply The equilibrium in this economy is illustrated in Figure 11 The width of the diagram is determined by, A is measured from left to right while M is measured from right to left The marginal product in $ in agriculture is drawn from left to right while the marginal product in $ in manufacturing is drawn from right to left Note that the wage w is determined by the interaction between a fixed supply and demand from two sectors A and M Note also that this is in effect the Harris-Todaro model of migration in the case where the wage is completely flexible in both sectors Now, knowing the value in the local currency ($) does not tell us that much We get more information if we measure everything in terms of units of goods With two goods we could use either good as the good that we use when measuring et us use the agricultural good (bags of corn) when measuring the value of production and the value of the wage By dividing on both sides of the equilibrium conditions by the price of food p A the equilibrium conditions becomes equal to x A = w/p A and x M p M /p A = w/p A The value of the marginal product measured in bags of corn should in each sector be equal to the value of the wage measured in bags of corn Then Figure 9 will change to Figure 12 12

13 Figure 11: Allocation of labour between Agriculture and Manufacturing value in $ value in $ A x A p A x M p M w w M Figure 12: The wage income meassured in bags of corn bags of corn bags of corn A x A x M p M /p A w/p A w/p A 13

14 Figure 13: Trade liberalization and structural shifts bags of corn bags of corn w/p A x A x M (p M /p A ) T A w/p A The figure is almost the same but now the interpretation is different Note for example that area below the w/p A line is total wage income in terms of bags of corn Hence, it captures how much the workers (and their families) can eat and is thus a measure of standard of living Until now we have not discussed how the prices are determined Assume for simplicity that they are determined by domestic demand in a situation with no trade Now, what happens if the country opens up for trade? Assume that the trade implies that both agricultural and manufacturing goods can be bought and sold at the world market at fixed prices et the relative prices at the world market be (p M /p A ) T and let the relative prices without trade be (p M /p A ) I,where T indicates trade and I indicates isolation If (p M /p A ) T < (p M /p A ) I, manufacturing goods are relatively cheaper at the world market and it makes sense to start exporting agricultural products and importing manufacturing products In this case the country has comparative advantage in the production in agricultural goods For a poor country, this may be a realistic response to trade liberalization Anyhow, this is the view of the IMF: I would like to see the markets of the industrialized countries opened So that these countries, with people who are poor and can produce agriculture, are able to export That s what would get them out of poverty Stanley Fischer (2001) The new rulers of the world Carlton Television td ets assume that it is indeed the case that (p M /p A ) T < (p M /p A ) I, then in Figure 12 the x M p M /p A curve would shift downwards as illustrated in Figure 13 where the dotted curve is the one that existed in the case without trade, ( x M (p M /p A ) I ) Three effects are immediate Demand from labour in manufacturing decreases and labour is shifted to 14

15 agriculture (ie urban to rural migration) As a result the wage (in terms of bags of corn) drops Profits in agriculture increase while profits in manufacturing decrease Another way to put it is that owners of land gain while owners of manufacturing capital lose The wage in terms of corn drops Does that mean that the workers lose? Not necessarily If workers also consume manufacturing goods they will benefit from the lower price and that will compensate somewhat the welfare loss and possibly give a gain For the country as a whole there is a gain The gain is captured by the shaded triangle The triangle captures bags of corn in excess if the country after trade reform and reallocation of labour wants to consume exactly what they did before the trade reform The argument is as follows After trade reform, if the country do not reallocate labour, they can consume the same amount of manufactures and agriculture as before - that s trivial But without reallocation of workers the marginal productivity will be higher in agriculture than in manufacturing The difference is the height of triangle at the left hand side As workers are moved from manufacturing to agriculture this gap is reduced until the new equilibrium The total gain, measured in bags of corn, from realocating workers is captured by the shade triangle To sum up: Given the assumptions of this model (not all are spelled out) A trade reform that leads to increased agricultural production has the following implications 1 Owners of capital in manufacturing lose (a lot) 2 Owners of land gain (a lot) 3 The labour may win or lose If they primarily consume agricultural goods they lose 4 The country as a whole gains This gain is small compared to the different groups gains and losses it is a triangle versus rectangles If trade reform instead implied increased production of manufactures and less production of agriculture, all the gains and losses would change sign, so that owners of capital win, owners of land lose, while labour probably win if they primarily consume food Also in this case the country as a whole would gain Why is this interesting? First of all, for better or worse, it is an influential framework for thinking about trade The arguments about comparative advantage pops up everywhere Second, the model illustrates starkly the conflict between distribution and over-all gains The reshuffled income between groups are larger in size than the over-all gain This result is often forgotten Third, it can be a good starting point for discussing trade reform under other assumptions For example: What if the workers own land? What if capital can be moved from manufacturing to agriculture? What if there is unemployment? Is it possible to compensate people? Is it possible to form alliances in favor of/ against trade liberalization? 15

16 Should we trust governments of poor countries when they claim that their country wants trade reform? Should we trust Norwegian farmers when they claim that they are against import of food because of a concern for the poor countries? What if there is increasing returns in manufacturing (learning by doing)? 10 Sustainable debt There are many countries in the world that have debt levels that are far above what they possibly can handle For these countries some kind of debt reduction is unavoidable Given that some countries should get debt relief it is essential to decide what debt level a country can possibly handle One important principle in debt relief is that it should be once and for all so that the country do not end up in similar problems after a year or ten The relief should bring the debt down to a level that is sustainable Sustainable debt can be defined in a number of ways One definition is that it is a level of debt such that the debt does not grow faster than GNI Hence it should be possible to hold the DEBT/GNI ratio constant over time That implies that if the growth rate of GNI is 3% a year the growth rate of DEBT should be no more than 3% a year The growth of the debt is determined by many factors Two important factors that I will focus on is the 1) export surplus and 2) interest on the existing debt (r DEBT where r is the rate of interest) Abstracting from other factors it follows that Growth in DEBT=r DEBT export surplus Assume that the expected growth rate of GNI is g From the definition above, the DEBT is sustainable if the growth in DEBT is equal to g DEBT Assume that the export surplus realistically can be a fraction a times the GNI Hence, a requirement for sustainable debt (DEBT SUST ) is that g DEBT SUST = r DEBT SUST a GNI DEBT SUST = S = a GNI r g Sufficient debt relief then implies bringing the debt level down to the level DEBT SUST, or to put it differently bringing the debt to GNI ratio down to S What determines S? Assume that a = 001 (that the export surplus is expected to be positive and equal to 1% of GNI) and assume that r = 007 (7%) then S = g If the growth rate is zero (g = 0) then S = 14%, if g = 2% then S = 20%, if g = 5% then S = 50%, if g = 6% then S = 100% (If the growth rate is large, g > 7%, then a can be 16

17 negative That implies that if the growth rate of GNI is higher than the interest rate it is possible to have a small export deficit at the same time as the debt is sustainable The important condition is that debt does not run faster than the GNI) Anyway, the main message is that the answer to the question What level of debt is sustainable? depends critically on the assumptions regarding r, a and g If one for example is too optimistic with regards to the growth rate g and expect g = 6%, a debt ratio of 100% may appear sustainable Debt relief based on that premise will prove not to be sufficient if g turn out to be 2% instead (in which case only a debt ratio of 20% is sustainable) In the ongoing debate between IMF Word Bank and the heavily indebted countries about debt relief the assessment of what the sustainable debt level is for each country is one of the main points Note that the countries that want maximum debt relief is best served by being pessimistic with regards to growth and export surplus potential Problems 1 Consider the case where the marginal product curve is x 1 = (P1) a) Draw the curve b) Derive the marginal product when 1 = 4 c) Shade the total product when the number of workers is 1 = 4 and assess the value d) Derive the expressions for the average product and the total product for all levels of 1 Use the result to calculate the total product when 1 = 4 Compare with c) e) Derive the value of 1 for which x 1 is zero f) Assume that the total available labour is = 10 Under central command what is optimal value of 1? g) Assume that there is alternative employment with fixed marginal product equal to 5 Under central command what is optimal value of 1 (and 1?) h) Under f) and g) what is the resulting 1 if P1 is a commons resource Illustrate the efficiency loss i) Under f) and g) what is the outcome if P1 is a factory owned by a profit maximizing owner setting 1 and paying as little as possible Illustrate the income distribution between factory owner and workers 2 Consider the case where total product is independent of employment 1 17

18 Y = 10 (P2) a) Draw the total product curve b) Derive the expressions for the average product for all 1 c) Assume that there is alternative employment with fixed marginal product equal to 5 Under central command what is optimal value of 1 (and 1 )? What will be the resulting 1 when P2 is a commons resource 3 Consider the case where there are two alternative sectors with profit maximizing owners in both sectors and marginal product as follows x 1 = x 2 = 5 2 (P3a) (P3b) a) Assume that total labour supply is = 9 Derive the equilibrium allocation of labour b) Assume that sector 1 is turned into a commons resource Derive the equilibrium allocation of workers c) illustrate with shading how going from a) to b) affected efficiency and income distribution 4 Consider Figure 127 in Ray s book Draw a marginal production curve and two wagecurves (opportunity cost) that illustrates the exact same message regarding and 18