Department of Economics Queen s University. ECON835: Development Economics Instructor: Huw Lloyd-Ellis

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1 Department of Economics Queen s University ECON835: Development Economics Instructor: Huw Lloyd-Ellis ssignment # nswer Key Due Date: Friday, November 30, 001 Section (40 percent): Discuss the validity of the following Short Statements. Your discussion should be concise (no longer than a page) and should use examples and diagrams where appropriate. ll questions are worth 8 percent. 1. When imperfect credit markets impose constraints on occupational choice, the distribution of wealth can affect per capita output. If there are diminishing returns to wealth in production, then transferring one unit of wealth from a rich entrepreneur to a poor entrepreneur will increase output and profits, because the poor entrepreneur has a higher marginal product. If credit markets worked perfectly, the rich entrepreneur would lend to the poor entrepreneur at a mutually agreeable rate of interest. If credit markets are imperfect however, this trade may not occur. s a result, it is possible that the poor agent may find entrepreneurship less profitable than working at the market wage. It follows that there will be fewer entrepreneurs than if the distribution of wealth were more equitable, and hence, lower per capita output (see Lloyd Ellis and Bernhardt, 1999).. The skewed distribution of ownership in many Latin merican countries during the early part of the twentieth century may have constrained it from shifting from agricultural to industrial production. The case of Latin merica, especially rgentina, at the beginning of the last century is often viewed as an example of the market size effect described by Murphy, Shleifer and Vishny (1989). On average, some of these countries were quite wealthy relative to the rest of the world at the time. However, the distribution of ownership was skewed towards a small upper class and a large fraction of the remainder were landless and owned few assets. Some argue that the reason these countries did not shift their production from agriculture to industry as rapidly as Europe and North merica, was because their small middle class was not sufficient to generate a large enough market for domestically produced consumer durables. s we have seen, without a sufficiently large middle class the big push of industrialization may not be realized. Many of these countries 1

2 have experienced internal strife throughout this century (e.g. revolutions and counterrevolutions, coups, wars, etc.) which have undoubtedly held back the development process as well, but even these may, at least in part, be attributed to the skewed distribution of ownership. 3. Neoclassical growth theory is not a useful theory of economic development. Neoclassical growth theory (i.e. the Solow model) explains differences in per capita income as being due to differences in the rate of capital accumulation. ccording to currently available data, and under reasonable parameter restrictions, cross country differences in savings rates are nowhere near enough to explain the vast differences in output per worker that exist throughout the world. Mankiw, Romer and Weil argue that when the Solow model is augmented to allow for human capital accumulation, the extended model does a pretty good job of accounting crosscountry differences. However, their regression results are difficult to interpret and are subject to omitted variable biases. Moreover, the model of human capital accumulation which they adopt is problematic as it assumes that human capital is accumulated in exactly the same way as physical capital. Quantitative analyses such as that of Prescott suggest that even allowing for variations in human capital investment does not help the model account for differences, under reasonable parameter settings. One could, of course, account for cross country differences by allowing TFP to vary across countries, but then the model wouldn t be explaining anything since it assumes that TFP growth is exogenous. 4. If schooling choices are made optimally, then measures of human capital should not be correlated with measures of total factor productivity. Optimal schooling choices should (in part) reflect the future returns from having greater education relative to the current costs of going to school. Part of those returns are presumably the future steam of wages and part of the costs include the wages foregone from attending school or college/university. In an economy in which TFP growth is anticipated to be rapid, expected future wages, for a given education, will be high relative to current wages. Thus, one might expect investment in human capital to be high in countries where TFP growth is high. This creates problems of interpretation for the regression analysis of Mankiw, Romer and Weil, because it implies that investment in human capital is likely to be correlated with the residual TFP across countries, so that the parameter estimate on this variable will be biased upwards. 5. s average incomes rise, households will optimally respond by having fewer but more educated children. ccording to Becker s (1960) theory the impact of an increase in income on the number of children is generally ambiguous. If it is an increase in non labour income and children are viewed as normal

3 goods, then such an increase will tend to lead households to have more children. If it is an increase in labour income, however, the impact is in general ambiguous because although households can afford more children (the income effect), the opportunity cost of having children (due to time not working) has also risen. More generally, households are likely to care about the well being of the their children and not just the number. In this case, they will also care about the resources allocated to each child (e.g. their education) since this will, in principle, give them greater incomes/utility. For example, suppose that a child s utility depends on the resources allocated to her, R. Ifthenumberof children is N, then total household utility might be something like: U(c, R, N) =u(c)+v(r, N), where c is household consumption. Where u( ) and v( ) represent sub utility functions. The budget constraint is c+rn = y, where y is household income. In this case, an increase in income may lead to a quality quantity trade off in that above some threshold, household s may prefer to allocate more resources per child rather than have more children. Section B (60 percent): nswer the following Long Questions. They are of equal value. B1. Pim and her three sisters own a small farm in the agricultural sector of the land of Grim. They work equally hard, and the value of their output measured in the local currency, nice, 4000 nice, which they divide equally. The urban sector of Grim has two kinds of jobs. There are informal jobs which anybody can get, which pay 500 nice, and there are formal jobs which pay 100 nice. The probability of getting these jobs depends on the proportion of such jobs to the urban labour force, exactly as in the Harris Todaro model. (a) ssume that Pim compares her own expected returns in the two sectors and there are no costs of migration. Calculate the threshold proportion of formal jobs to urban labour force that will just deter Pim from migrating. Let the probability of getting a formal job be p. Thisisalsotheratioofformaljobstourban labour force. The threshold value of p is implicitly given when the expected wage from migration is just equal to her current income: 100p +500(1 p) = 1000 p =

4 (b) The full production function on Pim s farm is given in the following table. Number working Output on farm (in nice) One sister 1500 Two sisters 500 Three sisters 3300 Four sisters 4000 Suppose that Pim and her sisters seek to maximize their total family income, instead of Pim simply acting to maximize her own. ssume that the threshold proportion that you derived in (a) actually does prevail in the urban sector. Now prove that Pim will migrate. If p = 5 7, then if she migrates her expected income is The income of the remaining sisters is 3300, so the total expected family income would be Since this exceeds 4000, Pam will migrate. (c) Will any of Pim s sisters also wish to migrate? Given that Pam has migrated, if one more sister migrates, their expected income is 000. The remaining sisters earn 500, so that total family income would be Now if a third sister migrates their expected income would be =4500, so the third sister would be just indifferent between migrating and remaining put. If she were to migrate, the fourth sister would not migrate since family income would fall to (d) Provide a brief description that uses your economic intuition to contrast cases (a) and (b). The marginal benefit from one sister migrating is a constant at The private marginal (opportunity) cost of migration to Pam is However, when she migrates this has a positive externality on her sisters due to the fact that are diminishing marginal returns to labour in production. Thus, the social marginal cost of migration (where society here is the sisters) is less than the private marginal cost. B. Consider an economy, like that considered by Murphy, Shleifer and Vishny (1988), consisting of three (representative) households. Each household supplies 1 unit of labour which could be used either in manufacturing or agriculture. Household 4

5 1 owns no shares, household owns a fraction ˆγ < 1 of the claims to both manufacturing firm profits and agricultural rents, and household 3 owns the remaining 1 ˆγ > 1. (a) The agricultural sector produces output using only labour according to the production function Y =L 1. Derive the agricultural profit function, π (L ), and wage function, w(l ) implied by profit maximization. Landowners maximize π =L 1 wl The necessary condition for a maximum is It follows that and dπ = L 1 dl w =0. w(l )=L 1, π (L )=L 1 L 1 L = L 1. (b) Let z =1be the maximum food requirement of all households. ssuming that w<z, show that, in equilibrium, the total amount of labour effort in agriculture is L ' (Hint: you will have to use the quadratic formula). Verify that this implies that w<z. Equilibrium in agriculture occurs when total agricultural income equals total spending on food: w(l )L + π (L ) = zn + w(l )(L N) L 1 = +L 1 Multiplying through by L 1 yields L L 1 1=0 Let x = L 1, then this is a quadratic equation in x. pplying the quadratic formula yields Thus, x = = 1+ 3 L =(1.37) = =1.37

6 (c) Manufacturing production is the same as in Murphy, Shleifer and Vishny. The fixed labour requirement for the modern technology is C =1and the traditional technology is half as productive as the modern technology: α =. Show that if all sectors up to Q industrialize, only household 3 will demand output from the Qth sector. Since they limit price traditional firms out of the market, so that p = αw, the profits of modern firms are given by π = αwx wx wc = w[(α 1)x C], where x isthedemandfortheirproduct. IfallsectorsuptoQ industrialize, this means that firms just earn zero profits in sector Q, and the total number of households that buy this good is given by N = C α 1 =1. It follows that the demand for the Qth good comes from the richest household 3. (d) Derive the MM curve for this economy. How do the equilibrium profits depend on the value of ˆγ? Explain the intuition for this relationship. Since household 1 buys only food and household 3 s expenditures covers the fixed costs of all industrial firms, the expenditure of household generates pure profits for modern firms. Since householdbuys1ofeachgooduptoq, these pure profits are aggregate to π = αwq wq. Since the total expenditure of household must equal its income, Q is determined by Substituting for Q yields z + pq = w +ˆγ(π + π ) Q = w +ˆγ(π + π ) z αw µ α 1 π = [w +ˆγ(π + π ) z] α π = 1 ) ˆγ(π + L 1 ) (1 L 1 Solving for π yields the MM-Curve π = ˆγL 1 (1 L 1 ˆγ In general equilibrium, it follows that π = 1.37ˆγ 0.7 ˆγ 6 ).

7 Clearly, π is increasing with ˆγ. The bigger the share of profits going to the middle class (which is household as long as ˆγ < 1 ), the bigger the demand for industrial goods. This in turn yields greater profits which results in even greater demand. Thus, the MM curve reflects a multiplier effect which is increasing in the profit share of the middle class. B3. n economy produces final output using capital, K, andlabour, L, according to the technology Y = K α (L) 1 α, where denotes the effectiveness of labour. Total output is growing at the rate of 5% per year. The rental rate per unit of capital is equal to 0.1 units of final output. The physical capital output ratio is 3:1. The stocks of capital and population are growing at the rate of 3 and % respectively. ssume that everybody works. (a) Under the assumption that all output is paid in wages and rent, calculate the implied shares of capital and labour in national income. The α = rk =0.1 3=0.3 Y (b) Using standard growth accounting techniques (e.g. Hall and Jones, 1999), estimatetheimpliedrateofgrowthintheeffectiveness of labour in this economy. Thegrowthofoutputisgivenby Y = α K +(1 α) +(1 α) L Y K L = 1 Y 1 α Y α K 1 α K L L Since the capital output ratio is constant, the capital stock must be growing at the same rate as output. ssume the workforce is growing at the same rate as the population. Then = = Suppose that the effectiveness of labour is given by = TH,whereT is TFP and H is human capital. The effect of an increase in schooling on an individual i s wage within the economy at a given level of technology is estimated to be given by ln w i =0.1 s i. (c) ssuming that the economy is approximately competitive, how could this information be used to construct an index of aggregate human capital growth? 7

8 In a competitive equilibrium, the wage is given by the marginal product of a unit of human capital is: v =(1 α)k α T 1 α (HL) α which depends on aggregate variables only. The wage of an individual with human capital h i could then be expressed as w i = vh i. ccording to Mincerian wage regressions, the log of real wages is approximately linearly related to years of schooling, so we can think of a change in the log of human capital as being linearly related to a change in years of schooling: ln h i =0.1 s i. It follows that a reasonable first approximation to an index of aggregate human capital might be something like H = e 0.1E, where E denotes the average years of schooling in the working population. Thus the growth rate of human capital is given by H H =0.1 E (d) If average years of schooling increases by 0.1 years per year, decompose the growth in into that component arising from TFP growth and that arising from human capital accumulation. Fromtheabove,humancapitalgrowsattherate0.1 0, 1=0.01, or 1% a year. It follows that must TFP grow at the rate T T = H H = = 0.0, or % per year. 8