SOLUTIONS TO MIDTERM EXAMINATION

Transcription

1 Ec 320, Fall 2007 Dilip Mookherjee SOLUTIONS TO MIDTERM EXAMINATION 1. Indicate whether you agree or disagree with the following statements, whether partially or fully, or subject to suitable qualifications or exceptions. In each case provide a brief explanation for your answer. (a) The Harrod-Domar model states that a country s growth rate of per capita income depends on its rate of savings, whereas the Solow model states that it does not. The Harrod-Domar model does state that the growth rate depends on the savings rate. The Solow model states that the short run growth rate depends on the savings rate, while the long run growth rate is independent of the savings rate. (b) The hypothesis of unconditional convergence can be empirically tested by plotting the growth rate of different countries over the period against their growth rates over the period and checking if there is a downward sloping relation between the two variables. Disagree. Unconditional convergence can be tested by plotting the growth rate over against the level of per capita income in 1960 and examining whether the relationship is negative. (c) The available statistical evidence from longitudinal country studies concerning the correlation between changes in inequality and changes in per capita income over time indicates no relationship between per capita income and income inequality. Agree: the analysis of Deininger and Squire, and of Fields and Jakubson, of longitudinal time series evidence for any given country indicates no relationship between per capita income and inequality. 1

2 (d) The available statistical evidence concerning the experience of any given country over time indicates no relationship between per capita income and poverty (as measured by the head count index). Disagree: the evidence for a large number of developing countries over the period between 1970 and 1990 indicates that growth was associated with a significant drop in the head count index. (e) The evidence on relation between wages and height of Brazilian workers in the Strauss- Thomas study indicates that most of the correlation between height and wages is accounted for by the causal impact of height on worker productivity. Strauss and Thomas use instrumental variable methods (using food prices, nonlabor income etc. as instruments for height) to identify the impact of height on wages; they find a 1% increase in height leads to a 2.4% increase in wages, which is 60% of the correlation between the two variables. So most of the correlation is accounted for by the impact of height on productivity. 2. (10 2=20marks) Answer any two of the following. (A) Consider the Lewis model of a labor surplus economy with a traditional and modern sector, which is currently in the first phase of development. Suppose that the government mandates a minimum wage (which exceeds the wage currently paid) which must be paid by all employers in the modern sector. Describe the effect of this policy on (i) the extent of migration from the traditional to the modern sector; (ii) the rate of growth of per capita income in the economy. (You may restrict your attention to the short run impact, when the country continues to operate in the first phase with surplus labor in the traditional sector.) (i) A minimum wage above the prevailing market wage will raise the cost of labor to employers in the modern sector. Given that the demand for labor in the modern sector is downward sloping, this implies that the level of employment in the modern sector will fall. With fewer jobs in the modern sector, there will be a reduction in the extent of migration from the traditional sector. 2

3 (ii) The increase in the cost of labor will reduce profits in industry. Since savings and investment in the Lewis model is a constant fraction of industry profits, the policy will cause a reduction in investment in the modern sector. Since growth in the Lewis model is driven by the investment in the modern sector, and the resulting migration from the traditional sector to the modern sector, this will slow down the rate of growth in the economy as a whole. (During the first phase, the price of food does not change, so any effects operating through the price of food can be ignored.) (B) Explain the effect of higher population growth rates on the growth rate of per capita income alternatively in the context of the (a) Harrod-Domar, (b) Solow, and (c) Lewis models, distinguishing carefully between short term and long term effects. In the Harrod-Domar model, a higher population growth rate unambiguously reduces the rate of growth (in both the short and long run). Assuming zero depreciation, for instance, the rate of growth g of per capita income in the Harrod-Domar model is given by g = s θ n 1+n where s is the savings rate, θ is the capital output ratio, and n is the population growth rate. So the higher is n, the lower is g. Since the short run and the long run rate of growth are the same, the same effect operates on both. In the Solow model, in the long run the amount of capital per head does not grow, owing to diminishing marginal productivity of capital. So the long-run rate of growth is always equal to the rate of technical progress, which is assumed to be exogenous, and thus independent of the savings rate. So there will be no effect at all on the long-run growth rate. In the short run, however, increases in capital per head do contribute to growth, if the country happens to be below the steady state amount of capital per head. Then for exactly the same reason as in the Harrod-Domar model, the short run growth will become smaller when population grows faster. In the Lewis model, the effect depends on which phase the economy happens to be in. If it is in the first phase, the effect on the short run growth rate is likely to be negative, as a higher population increases the demand for food, and thus drives up food prices (which 3

4 in turn raises the cost of labor in the modern sector, reducing migration, industrial profits and investment). Later, however, higher population growth relieves the labor scarcity (that characterizes the second and third phases) which slows down the growth process; the effect on the long run growth rate is less adverse than on the short run growth rate, and may even be positive. (C) An economy has a total population of 500 workers. Any given person can earn a constant wage of $1 in the agricultural sector. In the urban sector there are two factories producing an industrial good and sells it at a constant price. Each factory has a marginal revenue of y if it employs y workers; and takes the urban wage rate as given. Workers incur no transport cost to move between the agricultural and urban sectors. (a) Explain how labor will be allocated in the economy if urban wages adjust flexibly to equate supply and demand on the urban labor market. (b) How does the labor allocation change if the government mandates a minimum wage of $4 in the urban sector? (c) Explain how your answer to (b) changes one additional factory enters the urban sector. (a) With zero transport costs and flexible urban wages, the equilibrium wage in the urban sector will equal the agricultural wage of $1 (assuming the urban labor market clears at this wage). At a wage of $1, each factory will hire workers upto the point where y =1, or y = 30. Then total urban labor demand equals 30 2 = 60, less than total supply of workers. So the equilibrium allocation will involve 60 workers employed in factories, and the remaining 440 workers in agriculture. (b) With a minimum wage of $4, each factory will hire upto the point that 10.3y =4 or y = 20. Then there must be urban unemployment: otherwise the supply of labor to the urban area will be 500 as the urban wage exceeds the rural wage. The probability of finding a job in the urban sector will be p, such that the expected wage in the urban area 4p equals the rural wage of 1, or p =0.25. So the urban unemployment rate will be 75%. There will be 40 workers employed in factories, 120 will be unemployed, and the remaining 340 will remain in the rural sector. 4

5 (c) With three factories, urban employment will increase to 60, urban unemployment to 180, and the remaining 260 workers will be in agriculture. 5