Universidade Católica Portuguesa Economics Program

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1 Universidade Católica Portuguesa Economics Program Economics of Social Policy Test I Miguel Gouveia Spring 1999 I. Choose two very short answer questions (1 page max each). (2.5 points each) 1. What is specific egalitarianism? Provide examples. 2. What is consumer sovereignty? What is paternalism? Why are these concepts relevant for social policy? Give real world examples in support of your answer. 3. Explain what a merit good is and present a Public Choice criticism of public provision of goods justified by merit good arguments. Give an example. 4. What is the most important criticism to the Rawlsian theory of justice presented by Nozick? II. Answer both questions (2 page max each). (3 points each) 5. Both expenditures on computers and expenditures on health have been increasing fast in OECD countries. Why do we worry about health expenditures and not computer expenditures? 6. When measuring the distribution of welfare, we sometimes study the distribution of flows, other times the distribution of stocks. Are capital gains a stock or a flow? Define both concepts, give other examples of stocks and flows relevant to the distribution of welfare. III. Answer the following question. 7. An econometrician estimated the following Engel curve for annual household expenditures on cosmetics. Exp= * Inc -70* N 5 100* N *Inc *(N 15 +N 5 ), where Exp is expenditure and Inc is income, both measured in Euros. N 5 is number of children under 5 years of age and N 15 is the number of children aged between 6 and fifteen. Normalize a childless couple to have an equivalence scale of 1 and consider that the income level for the childless household relevant for comparisons is a) Briefly define equivalence scale and explain what is Rothbard s methodology for estimating them. ( 2 points)

2 b) Provide Rothbard equivalence scales based on the regression presented for families composed by a couple plus (2 points) i) N 5 =1, N 5 =0 ii) N 5 =0, N 5 =1 iii) N 5 =N 5 =2 IV. Answer the following harder question. 8. Directorland is a democracy where taxation and redistribution decisions are made by majority rule voting. In particular, a majority decides to tax a minority by a proportional income tax at rate t and redistribute the tax revenue in a lump sum to all majority members. Preferences are given by U= C +ln(1-h), where C is consumption and h is labor supply. Agents are characterized by their productivity W (equal to wage rates), which are uniformly distributed in the interval [2,4]. The budget constraint for each citizen in the minority is: C=w(1-t) h, and in the majority is C=wh+L, where L is the lump sum transfer. a) Derive the labor supply, gross income, net income and tax payment for an agent with wage rate w in the minority and for an agent in the majority. (2 points) b) Assume that the political equilibrium is equal to Stigler s, i.e. the bottom 50% + ε of the wage distribution are the majority. What is the government (tax and transfer program) budget constraint? (1 point) c) What is the political equilibrium in terms of the tax rate chosen? Could it be sustained if people could hide their ability and pretend to be of other ability level? (2 points)

3 Solutions to the test W ~U[2,4]. This means f ( w) = 1/ 2. Distribution implies that mean and median voter has w=3. U= C +ln(1-h) Minority C=w(1-t) h, Majority is C=wh+L a) Labor supply, etc. U=w(1-t)h+ln(1-h) Labor supply in minority U h 1 = w( 1 t) = 0, 1 h Labor supply in majority 1 1 h = w 0 if w < 1 gross gross income income in minority in majority 1 1 h = (1 t) w 0 if w(1 t) < 1 1 y = w 1 t y = w 1 consumptio consumptio n in minority n in majority c = w(1 t) 1 c = w 1 + L Individual tax T = t y t = tw 1 t For the record, individual tax revenue maximizing rate is (1 t) + t T ( y( w)) => w = 0, 2 (1 t) t Max t * = 1 1 w b) government budget constrains Expenditures = 3 2 Lf ( w) dw = L 2

4 Revenues = constraint is 2 5t 7t L = 2(1 t) t 5t 7t ( tw ) dw =, so we have that the government budget 2 1 t 4(1 ) 3 t c) The equilibrium value for t and L is given by the value of t that maximizes L L t = 5 14t + 7t 2(1 t) = 0 t 2 14 ± 14 2*7 4*5*7 = 2*7 t = L=0.7583

5 Universidade Católica Portuguesa Economics Program Economics of Social Policy Test II Miguel Gouveia Spring 1999 I. Answer all questions (1 page max each). (1.5 points each) 1) Provide one argument against and one in favor of social policies relying on in-kind transfers as opposed to cash transfers. 2) What is the difference between defined benefit and defined contribution pension plans? 3) Explain how you would construct a poverty line based on the notion of absolute poverty. II. Answer two of the following questions (2-page max each). (3 points each) 4) Two possible indexes of inequality are: C10: The total income share of the poorest 10% of the population Maximum Income Minimum Income Relative Range: Average Income Are these indexes good or bad? Explain, based on objective criteria. 5) It is often useful to analyze empirical income distributions by decomposing their inequality measures. What are the two main types of decomposition, how are they carried out, and what kind of questions can they answer? 6) "There may be problems with the transition to a funded system of old-age pensions, but in steady state the return to a worker contributions will always be better than pay-as-you-go". Is this true? Explain. III. Answer the following question. Equivalent Income Individuals ) Consider the income distribution in the table above. a) Construct a generalized Lorenz and a Lorenz curve for the income distribution (consider only the 5 points given). (1)

6 b) Calculate the Atkinson index with ε=1. (1) c) Calculate the poverty measures P0, P1 and P2. (1.5) d) Calculate the Gini index for the distribution. (1.5) IV. Answer the following question on the maturation of old age pension systems. Consider a population homogeneous in all dimensions except age. Everybody has annual earnings W, everybody lives for M years and everybody works for R (R<M) years. Population is stable (the age density function is f(age)= 1/M. The old age pension is b. Define t e to be the equilibrium contribution rate for a given year, i.e. the payroll tax rate that produces enough revenue to pay the pensions due in that year Consider what happens if we introduce in this economy a pay-as-you-go social security system where no social protection existed before. 8) a) If at time t 0 the PAYGO system is introduced, with everybody with age over R receiving a fixed pension b (regardless of contributions) and everybody under age R contributing t e W, determine the level of t e. How will the equilibrium contribution rate change over time? (1.5) b) Suppose now that only the active workers at time t 0 are entitled to a pension in the amount b. Find the equilibrium contribution rate and how it changes over time. (1,5) c) (Difficult). Suppose now that the old age pension is a function of how long the worker contributed, b=k L W, where k is a parameter (in Portugal it is 2%) and L is the number of years working and making contributions. If a social security system is introduced at time t 0, how will the equilibrium contribution rate change over time? What is its steady state level? (1.5)

7 Universidade Católica Portuguesa Economics Program Economics of Social Policy Test I Miguel Gouveia Spring 2000 I. Choose one very short answer question (1 page max each). (4 points) 1. Historically there are three important milestones in the development of social protection systems around the world. What are they are. 2. Briefly, describe what has been the technology impact on health care expenditures. 3. When measuring the distribution of welfare, we can study the distribution of expenditure or the distribution of consumption. What are the differences? Which one is a better measure of welfare? II. Answer one of the following two questions (2 page max). (5 points) 4. How would you estimate the contribution of the aging of the population to the growth of expenditures on health? What data would you need to do that? Provide numerical examples. 5. Two individuals have utility functions given by U i =xy U j =x 2 y. The total amount of good x available is 10 and the total amount of good y available is 20. Consider three allocations of resources (x i, y i ; x j,y j ) that are (5,10; 5,10), (6,8; 4,12), (3,13; 7,7). Which, if any, of these allocations are envy-free? Are any of the allocations efficient? Is any allocation fair? III. Answer the following question. (6 points) 6. Tealand is a country where citizens are very altruistic towards people poorer than themselves. a) In terms of the way altruistic preferences are formalized, describe three different types of altruism. b) The distribution of income in Tealand can be summarized in the following table. Construct the tax transfer scheme that corresponds to the altruistic preferences. Note that unlike what you saw in class, the number of people in each income class is different. You should follow the rule that transfers from one income class to another make an average member of the lower income class 3% closer to an average member of the richer class only taking into account pretax and pretransfer incomes. What are the marginal tax rates? Is the tax system you have found progressive? Income Frequency % % % % IV. Answer the following question (5 points) 7. There are three groups in a society, each with a third of the population. Group A members have a utility function given by U a = x.5 y.5 and income I a =12. Group B members have a utility function given by U b =x and income I b =9. Group C has a utility function U c =y and income I c =18. If a good is socialized it will be uniformly provided by government and financed by a proportional income tax. c) If both good x and good y have a marginal cost =average cost =1, what is the competitive allocation of resources (quantities of x and y for each group member)?

8 d) Assuming good x is socialized, what is the allocation of resources? Keep in mind that the choice of x will be given by the choice of the median voter and that the average income to be taxed will be 13=( )/3. e) Will good x be socialized if this society makes that choice in a referendum? Provide an intuitive explanation for your findings. (If you were unable to find the median voter choice in b) assume it is x=6).

9 Universidade Católica Portuguesa Economics Program Economics of Social Policy Test I Answers Miguel Gouveia Spring 2000 I. 1. a. In , Chancellor Otto von Bismarck of Germany established the first social insurance programs, sickness insurance, and paid sick leave plans supported by the compulsory contributions of workers and employers. In 1889 an old-age insurance program was added, to which the government also contributed. b. In the US, after the Great Depression of 1929, Roosevelt starts the New Deal which increased the role of the State. The Social Security Act of 1935 created a near universal and compulsory social security program dealing with disability, survivers, and old age pensions. Other legislation created a state -federal system of unemployment insurance. c. Great Britain instituted a national social insurance scheme, establishing a rudimentary unemployment and old-age insurance program in This program was greatly expanded and liberalized in 1925 and again after World War II when a program of "cradle-to-grave security," advocated by Sir William Henry BEVERIDGE, was adopted. This included the start of the National Health Service. 2. The case of technological progress and health care is marked by the distinction between process innovation versus product innovation. Product innovation (new goods and services, which in health care means new drugs, devices, procedures, diagnostic techniques, etc.) leads to rapid growth in health care costs and it has been very prevalent in health care. Process innovation increases productivit y and reduces costs of already existing goods and services and it has been very absent from health care, leading to Baumol s disease, i.e. health care relative prices go up over time. 3. According to life-cycle theories expenditures for any given year are also good proxies for the life-cycle welfare of individuals, since they anticipate lifetime income and expenditure patterns or profiles. A first problem about the use of expenditures comes from durable goods because they will generate consumption flows for a few years. These flows are what really determines welfare. One should annualize expenditures on durable goods to transform expenditure into consumption. A second problem comes from the public provision of goods and services. When comparing two distributions, the extent to which needs are satisfied by government is important. If transportation, health, education, etc, are free or heavily subsidized in situation A and are privately provided in situation B, comparing welfare distributions in A and B has to take that difference into account. II. 4. There is a simple but effective technique due to the US Congressional Budget Office. Each person over 65 costs, on average, k times the expenditure of a person under 65. This k and the population share over 65, whic h we can call x are the two crucial variables. Then, once you have these variables you can construct the time-series of the weighted average WA= (1-x)*1+x*k. The growth of the weighted average as x increases equals the growth of real per capita expenditures due to aging. Example: if k=4 and x=0.05 in year T then index is If x=0.1 in year T+10, then index is 1.3. The growth of the index is =1.3/1.15 1, about 13%. 5. The utility of the individuals in the current allocation and in the allocation where consumption levels area reversed is given by:

10 Initial allocation Utility of i at initial allocation Utility of j at initial allocation Utility of i at reverse allocation A=(5,10;5,10) B=(6,8;4,12) B=(3,13;7,7) Utility of j at reverse allocation Allocation A is envy free because it is symmetric In Allocation B, i does not envy j, but j envies i. In allocation C, i envies j and j does not envy i. Thus only the allocation A is envy free. To be fair the allocations must be envy free and efficient. Efficient allocations are on the contract curve and that means the marginal rate of substitution is the same for both agents. Initial allocation MRS of i at initial allocation MRS of j at initial allocation dy/dx=y/x dy/dx=2y/x A=(5,10;5,10) 2 4 B=(6,8;4,12) B=(3,13;7,7) The MRS's are never equal. No allocation in the list is efficient or fair. III. 6. Take the case of consumption good x and where utility of individual 1 depends on individual 2. In the case with two individuals we can have: U ( x1, x2 ) or U ( x1, U2) or U ( x1, t1 2) The first is paternalistic altruism, the second is non-paternalistic altruism (since there is consumer sovereignty) and the third is impure altruism or warm-glow altruism. a) We have to make a distinction between the transfer received by an agent and the transfer paid by an agent. The transfer received depends on differences in average incomes across classes, where the transfer paid depends on differences in average incomes across classes, on how many people are giving and how many receiving. The transfer between groups 1 and 2, T21=0,03*( )=30 is what each member of 1 receives from group 2 as a whole. Since there are 4 people in group 3 for each person in group 1 each member of group two pays 30/4=7.5. the complete set of transfers is given by Groups Receiving Paying 2-> > > > > > The next table gives the final result: Groups Tax Transfer Marg. Tax ,75% ,25% %

11 So the system has increasing marginal tax rates. Since it starts at zero taxes it is a progressive system. 7. a) In a competitive market B spends all his income on x, (9,0) and C spends all his income on y (0,18). As for A, his demand curve for x is x d =12/(2p x ), and for y is is y d =12/(2p y ). Since both prices equal 1, we have a symmetric basket of goods for A, (6,6). The total amount of x produced is X=15 and y produced is Y=24. b) If x is socialized, its uniform public provision will be financed from proportional income taxes on all incomes. Since there are three citizens, providing each citizen with x requires an income taxation rate t such that 3x=t( ), i.e. x= t 13. What are the preferred levels of x? For B, the preferred level is x=13 (t=100%). For C the preferred level is x=0. For A the preferred level is the one that maximizes utility. Given a tax rate t, the x=13 t, but we also have that y=12(1-t). The problem is: Max (1*13) 0.5 ((1-t)*12) 0.5, with solution t=0.5 or x**=6.5 Since A prefers x=6.5, B prefers x=13, and C x=0, the median is x=6.5, so this would be the choice for the public provision level of x when x is chosen by majority rule. c) We can now compare the utility of all agents under competition and under socialization, with the level of x is chosen by majority. Agents Utility with market Utility with socialization A B C 18 9 Socialization is defeated (A versus B,C) because tastes are too heterogeneous. Universidade Católica Portuguesa Economics Program Economics of Social Policy Test II Miguel Gouveia Spring 2000 I. Choose two very short answer questions (1 page max each). (2.5 points each) 1) There are three different ways of paying health care providers. Describe them and briefly explain their incentive properties. 2) Explain what are defined benefit and defined contribution pension schemes. 3) What is the relationship between equivalence scales and the poverty line? 4) What demographic indicator is more relevant to studying the future of social security pensions: the birth rate or the total fertility rate? Briefly explain why.

12 II. Answer two of the following questions (2 page max). (3 points each) 5) Explain the difference between the concepts of absolute poverty and relative poverty. 6) What are ex ante moral hazard and ex post moral hazard in the demand for health care? 7) What is the rate of return to worker contributions in a steady state social security system with pay as you go financing? Compare it with the rate of return in a funded system. III. Answer the following question. (4.5 points) 8) Minimum wage laws are sometimes defended on the basis that they are effective tools to fight poverty. a) What does Economics have to say about the effects of minimum wage laws on competitive labor markets and on poverty? b) Suppose the labor market is monopsonistic. Using the appropriate graphs, find the maximum level of employment that a minimum wage law can allow. How does it compare with the level of employment in a non-regulated but otherwise similar competitive labor market? c) The marginal productivity of labor (MPl) for a monopsonistic firm is MPl=10- L, where L is the quantity of labor. The labor supply in this market is L= w, where w is the wage rate. What is the monopsonistic equilibr ium level of employment if there is a minimum wage law setting the wage 20% above the unregulated monopsonistic level? IV. Answer the following question (4.5 points) 9) Imagine there are five individuals in a society with incomes 1000, 2000, 3000, 4000, a) Use 50% of the median as the poverty line. Define the three F (Foster s) measures of poverty and calculate them for this data. b) Define the Atkinson (ε=2) measure of inequality and calculate it for this data. c) Starting with the data provided, present a numerical example where the income distribution changes in such a way that poverty decreases but inequality increases.

13 Universidade Católica Portuguesa Economics Program Economics of Social Policy Test I Miguel Gouveia Spring 2001 I. Choose two very short answer questions (1 page max each). (2.5 points each) 1. What is paternalism? Provide examples in the area of social policy. 2. Compare product versus process innovation in the area of health care and discuss their implications for social policy expenditures. 3. Present two major differences between bismarckian and beveridgian welfare states. II. Answer both questions (2 page max each). (3 points each) 4. The following table has demographic and health expenditure data for three countries. Based on that data, what would be your estimate of the impact of population aging on health expenditures in the three countries? Country Health Exp factor over 65 Population % over 65 in 1980 Population % over 65 in 2000 Portugal 1, % 15.2% Sweden 2, % 17.0% Switzerland 4, % 14.4% 5. When measuring the distribution of welfare, we make a distinction between consumption flows and consumption expenditures. Explain why. In the year 2000 a household purchased a house (price: Euro), a car (price: Euro), groceries ( Euro) and received, free from government, health care services at a cost of 2500 Euro. What is expenditure and what is consumption in this particular case? Use the assumptions you feel are necessary to answer the question and state those assumptions explicitly. III. Answer the following question. (5 points) 6. An econometrician estimated the following Engel curve for annual household expenditures on cosmetics. Exp= * Inc -70* N 5 100* N *Inc *(N 15 +N 5 ),

14 where Exp is expenditure and Inc is income, both measured in Euros. N 5 is number of children under 5 years of age and N 15 is the number of children aged between 6 and fifteen. Normalize a childless couple to have an equivalence scale of 1 and consider that the income level for the childless household relevant for comparisons is Euro. Briefly define equivalence scale and explain what is Rothbard s methodology for estimating them. ( 2 points) Provide Rothbard equivalence scales based on the regression presented for families composed by a couple plus (2 points) iv) N 5 =1, N 15 =0 v) N 5 =0, N 15 =1 vi) N 5 =N 15 =2 IV. Answer the following question. (4 points) 7. Consider a case where there are only two goods in the economy: apples and oranges. Adam likes only apples and Eve likes only oranges. There are 10 apples and 20 oranges in the economy. Find a) the set of all envy-free allocations, b) the set of all efficient allocations and the set of all fair (both envy-free and efficient) allocations of apples and oranges. Suggestion: Use an Edgeworth Box to represent the problem.

15 Universidade Católica Portuguesa Economics Program Economics of Social Policy Test II Miguel Gouveia Spring 2001 I. Choose 2 very short answer questions (1 page max each). (3 points each) 1. What is fee-for-service? Explain its effects on the behavior and welfare of the economic agents concerned. 2. Briefly describe what is the steady state rate of return to workers of funded versus pay-as-you-go pension plans. 3. What is the economic concept of aversion to inequality? 4. There are three basic forces that lead to increasing expenditures on pensions. Explain briefly what they are. II. Answer all questions. (3 points each) 4. The following table has income data for a population. Income Frequency % % % % % a) Calculate two alternative poverty lines. For the next two questions your answers should rely on the median based poverty line. b) Define and calculate the poverty rate. c) Define and calculate F1 and F2 5. Using the table in question 4, calculate Atkinson s measure of inequality when the utility function is U=ln(y). What is the level of aversion to inequality in this case? 6. Assume that there is a negative income tax system applied to the incomes in the table of question 4. The transfer rule is B= * Gross Income. a) What are the minimum income guaranteed, the implicit marginal tax rate, and the critical level of income?

16 b) How much does this negative income tax system cost? c) Using you answers to question 4, by how much does this system reduce poverty? d) How would your answers to b) and c) change once you recognize the existence of incentive effects? III. Answer the following question. (5 points) 7. Consider a case where the utility function of a worker/consumer is given by C, where C is consumption (or net income). The consumer can stay in her regular job and earn 1200 with certainty. She can also take a chance and work in a third world country earning However, in the third world country there is a 50% probability she will contract a tropical disease that costs 1500 to cure. The disease has no pain and it is completely curable. a) If she does not have access to health insurance, will she take the job in the third world country? Explain your answer. b) If she has access to actuarially fair health insurance will she take the job in the third world country? Explain your answer. c) Define ex ante and ex post moral hazard. d) Suppose now that because of ex ante moral hazard, insurance is more expensive relative to the ideal situation. What is the utility loss if the probability of the disease increases to 52%? And to 60%? And to 80%? e) Can you find an income measure of the losses in d), that is an income amount that measures the welfare loss due to moral hazard?

17 Universidade Católica Portuguesa Faculdade de Ciências Económicas e Empresariais Economics of Social Policy Test I Miguel Gouveia Spring 2002 A. Short Answer questions. (Max 1 page, 2 points each) 1. What is the main difference between the financing of beveridgian and of bismarkian social protection systems? 2. Income, Wealth and Expenditure are three variables whose distribution has been studied by economists, statisticians and others. Which one do you believe to be the best as a measure of the welfare of households and individuals? 3. Explain what is Rawls s "veil of ignorance". 4. What are the two largest social protection expenditure categories in the European Union countries? Is the largest category the same across all EU countries? Explain. B. Problems. (4 points each) 5. Mr. Smith and Mr. Brown are altruistic neighbors. Mr. Brown s coconut consumption is Cb and Mr. Smith s coconut consumption is Cs. Brown s utility is Ub=2ln(Cb)+ln(Cs) and Smith s utility is Us=3ln(Cs)+ln(Cb). Given that there are 100 coconuts in their neighborhood, find the Pareto optimal allocations (i.e. the Pareto optimal distributions of coconuts). What would they be without altruism? 6. In Directorland, the distribution of income is a discrete uniform between 1 and 5, as shown in Figure 1. The politics of income redistribution follow the lines of Stigler s model of expropriation: a winning coalition (one with more than 50% of total power) taxes those outside at given rate t and its members share the revenues. Figure 1 Population shares 0,25 0,2 0,15 0,1 0,05 0 Income Distribution Income a) What is the redistributional equilibrium with the rule one person one vote? b) What is the redistributional equilibrium if each person s political power depends on her income, with power proportional to Income 2? c) What is the redistributional equilibrium if each person s political power depends on her income, with power proportional to 3,2-3/Income 2?

18 Economics Program Economics of Social Policy Test II Miguel Gouveia Spring 2002 I. Choose 3 very short answer questions (1 page max each). (3 points each) 1. Explain what is the equivalence scale elasticity. 2. Briefly describe what is the steady state rate of return to workers of funded versus pay-as-you-go pension plans. 3. What are the main four axioms that inequality measures must respect? Explain their meaning. 4. There are three basic forces that lead to increasing expenditures on pensions. Explain briefly what they are. II. Answer all questions. (3 points each) 4. The following table has income data for a population. Income Frequency % % % % % d) Calculate the Lorenz curve. e) The poverty line is defined to be Define and calculate the poverty measures F0, F1 and F2. 5. Using the table in question 4, calculate Atkinson s measure of inequality when the utility function is U=ln(y). What is the level of aversion to inequality in this case? 6. Assume that there is a negative income tax system applied to the incomes in the table of question 4. The transfer rule is B= * Gross Income. e) What are the minimum income guaranteed, the implicit marginal tax rate, and the critical level of income? f) How much does this negative income tax system cost?

19 g) Using you answers to question 4, by how much does this system reduce poverty? h) How would your answers to b) and c) change once you recognize the existence of incentive effects? III. Answer the following question. (5 points) 7. The unemployment rate in Portugal and in the USA has been similar for a long time. If the exit rate out of unemployment is x and the entry rate into unemployment is y what is the long run level of the unemployment rate? What is the mean duration of unemployment? Universidade Católica Portuguesa Faculdade de Ciências Económicas e Empresariais Economics of Social Policy Miguel Gouveia Spring 2002 B. Short Answer questions. (Max 1 page, 2 points each) 8. What is the main difference between the financing of beveridgian and of bismarkian social protection systems? 9. Income, Wealth and Expenditure are three variables whose distribution has been studied by economists, statisticians and others. Which one do you believe to be the best as a measure of the welfare of households and individuals? 10. Explain what is Rawls s "veil of ignorance". 11. What are the two largest social protection expenditure categories in the European Union countries? Is the largest category the same across all EU countries? Explain. B. Problems. (4 points each) 12. Mr. Smith and Mr. Brown are altruistic neighbors. Mr. Brown s coconut consumption is Cb and Mr. Smith s coconut consumption is Cs. Brown s utility is Ub=2ln(Cb)+ln(Cs) and Smith s utility is Us=3ln(Cs)+ln(Cb). Given that there are 100 coconuts in their neighborhood, find the Pareto optimal allocations (i.e. the Pareto optimal distributions of coconuts). What would they be without altruism? 13. In Directorland, the distribution of income is a discrete uniform between 1 and 5, as shown in Figure 1. The politics of income redistribution follow the lines of Stigler s model of expropriation: a winning coalition (one with more than 50% of total power) taxes those outside at given rate t and its members share the revenues.

20 Figure 1 Population shares 0,25 0,2 0,15 0,1 0,05 0 Income Distribution Income a) What is the redistributional equilibrium with the rule one person one vote? b) What is the redistributional equilibrium if each person s political power depends on her income, with power proportional to Income 2? c) What is the redistributional equilibrium if each person s political power depends on her income, with power proportional to 3,2-3/Income 2? Universidade Católica Portuguesa Faculdade de Ciências Económicas e Empresariais Economics of Social Policy Test II Miguel Gouveia Spring 2002 I. Choose 3 very short answer questions (1 page max each). (3 points each) 1. Explain what is the equivalence scale elasticity. 2. Briefly describe what is the steady state rate of return to workers of funded versus pay-as-you-go pension plans. 3. What are the main four axioms that inequality measures must respect? Explain their meaning. 4. There are three basic forces that lead to increasing expenditures on pensions. Explain briefly what they are. II. Answer all questions. (3 points each) 4. The following table has income data for a population. Income Frequency %

21 % % % % f) Calculate the Lorenz curve. g) The poverty line is defined to be Define and calculate the poverty measures F0, F1 and F2. 5. Using the table in question 4, calculate Atkinson s measure of inequality when the utility function is U=ln(y). What is the level of aversion to inequality in this case? 6. Assume that there is a negative income tax system applied to the incomes in the table of question 4. The transfer (B) rule to the poor is B= * Gross Income. i) What are the minimum income guaranteed, the implicit marginal tax rate, and the critical (zero transfer) level of income? j) How much does this negative income tax system cost? k) Using you answers to question 4, by how much does this system reduce poverty? l) How would your answers to b) and c) change once you recognize the existence of incentive effects?

22 Universidade Católica Portuguesa Faculdade de Ciências Económicas e Empresariais Análise Económica da Política Social Exame para Finalistas Miguel Gouveia Novembro 2002 A. Short Answer. (Max 1 page, 2 points each) 1. The transfers made by Acção Social to the needy in Portugal are predominantly in kind rather than in cash. Is this paternalism or are there other economic arguments to justify the predominance of in-kind transfers? 2. Explain what is Nozick s position on social justice. 3. Explain what is the equivalence scale elasticity. 4. Briefly describe what is the steady state rate of return to workers of funded versus pay-as-you-go pension plans. 5. There are three basic forces that lead to increasing expenditures on pensions. Explain briefly what they are. B. Problems. 6. The following table has income data for a population.. (4 points) Income Frequency % % % % % % a) Calculate the Lorenz curve. b) Calculate two poverty lines and explain how you defined them.~ c) Calculate the poverty rate for both poverty lines. d) Calculate F1 and F2 for one of the poverty lines you found in question 6.b 7. Using the table in question 6, calculate Atkinson s measure of inequality when the level of aversion to inequality is 1 and when it is 2. (2 points) 8. Assume that there is a negative income tax system applied to the incomes in the table of question 4. The transfer rule is B= * Gross Income. (4 points)

23 a) What are the minimum income guaranteed, the implicit marginal tax rate, and the critical level of income? b) How much does this negative income tax system cost? c) Using you answers to question 6.b, by how much does this system reduce poverty? d) How would your answers to b) and c) change once you recognize the existence of incentive effects?

24 Universidade Católica Portuguesa Faculdade de Ciências Económicas e Empresariais Economics of Social Policy Test I Miguel Gouveia Spring 2003 A. Very Short Answer questions. (Max 1/2 page, 3 points each) 1. What is the main difference between the financing of beveridgian and of bismarkian social protection systems? 2. What are merit goods? How can they be related to perverse income redistribuition interventions by governments? 3. Explain what is Nozick s position on social justice. B. Problems. (5.5 points each) Figure 1 Income Distribution % 16,0% 14,0% 12,0% 10,0% 8,0% 6,0% 4,0% 2,0% 0,0% Income 4. The population of the country Friendly are Us is altruistic. Before taxes and transfers the distribution on income is the one on Figure 1, with f=1/7. a. Explain what different types of altruism are there. b. Altruism leads to voluntary redistribution. Will it be Pareto efficient in this case? c. Imagine that, after all other potential problems are solved, altruism leads to each person making a transfer to people with lower incomes in the amount of 10% of the difference between gross incomes. What would the transfers and net incomes look like in the country Friendly are Us? 5. In the country Everyone for himself, the distribution of income is as shown in Figure 1. The politics of income redistribution follow the lines of Stigler s model of expropriation: a winning coalition (one with more than 50% of total power) taxes those outside at given rate t and its members share the revenues. d) What is the redistributional equilibrium with the rule one person one vote? e) What is the redistributional equilibrium if each person s political power depends on her income, with power proportional to Income 2? f) What is the redistributional equilibrium if each person s political power depends on her income, with power proportional to Income 1/2?

25 Universidade Católica Portuguesa Economics Program Economics of Social Policy Test I Answers Miguel Gouveia Spring 2003 I. 1. The main difference between the financing of beveridgian and of bismarkian social protection systems is that bismarckian systems rely on contributions based on labor incomes (social security contributions, the payroll tax) whereas beveridgian systems rely on general government revenues, i.e. the entire tax system. This means that taxes on capital income, on expenditure or on wealth also help finance social protection schemes in beveridgian systems. 2. Merit goods are those for which society (i.e. governments) decides that their value is different than the aggregate value individuals themselves attribute to them. They represent an instance of paternalistic action by governments with a less than full following of consumer s sovereignty. They can be related to perverse income redistribuitional interventions because the rhetoric of merit goods (for example opera, other cultural goods) can be used to justify subsidizing goods and services that are consumed disproportionably by the rich 3. Nozick rejects the veil-of-ignorance methodology to define justice because behind the veil of ignorance one can only discuss outcomes, end-states. But this excludes consideration of the processes of economic and social interaction. In Nozicks view the important aspect of justice is in the process not in the final outcomes. For him important each person is entitled to holdings at which she arrives in legitimate ways (voluntary transfers, work, exchanges, etc.) For example monopoly rents are not legitimate, but income earned in competitive markets is, no matter how large or how unequal the final distribution turns out to be. B. Problems. 4. a. We can consider pure altruism, where the welfare of a person depends on the welfare of the other, as judged by this second person. In this case we write 1 preferences as: U ( x1, U 2). In the second case the welfare of a person 1 depends on the welfare of the other, 2, as judged by person 1, that is in a 1 paternalistic way. In this case we write preferences as: U ( x1, x2 ).Finally, we can have impure altruism, with warm-glow effects. In this case case the welfare of a person 1 depends on the transfers he makes to the other person 1 2. In this case we write preferences as: U ( x1, t1 2). b. No. If we had only two people voluntary redistribution would generate a Pareto Optimum. With large numbers of individuals we will have a free riding problem and the outcome will most likely be inefficient. c.. Income Transfers Received Transfers Paid Net Transfer Net Income 1 2,1 0 2,1 3,1 2 1,5 0,1 1,4 3, ,3 0,7 3,7 4 0,6 0, ,3 1-0,7 4,3 6 0,1 1,5-1,4 4, ,1-2,1 4,9

26 5. a. The redistributional equilibrium with the rule one person one vote has the four poorest income groups together expropriating the 3 richest groups. If each person s political power depends on her income, with power proportional to Income 2, or to the square root of income as in c we have: Income Income 2 Income Sqrt 1 1 1, , , , , , ,646 Total ,478 Power >70 Power >6,739 b. Examples of coalitions: Coalition 6 and 7 7 and 5 4, 5 and 6 Power Per Cap Revenue 7,5 8 4, In this case the winning coalition is 7 and 5: it has enough power and the highest per capita revenue from expropriating the other incomes outside the coalition. c.. Coalition Power 7,382 7,331 6,882 6,827 Per Cap Revenue 3,500 3, In this case both coalitions 457 and 367 have enough power and have the highest per capita revenue from expropriation of outsiders. Since 457 has slightly more power it is the best choice, but 367 is also acceptable.

27 Universidade Católica Portuguesa Faculdade de Ciências Económicas e Empresariais Economics of Social Policy Test II Miguel Gouveia Spring 2003 A. Very Short Answer questions. (Max 1/2 page, 2.5 points each) 1. Briefly describe what is the steady state rate of return to workers of funded versus pay-as-you-go pension plans. 2. Explain what are defined benefit and defined contribution pension schemes. 3. What is the relationship between equivalence scales and the poverty line? 4. The Gini index for Sweden in 1990 was How was this figure produced and what is its interpretation? B. Problems. (5 points each) Table 1 Income Frequency % % % % % % 5. Using the data in Table 1: a. Calculate a poverty line using the methodology explained in class. b. Calculate the poverty rate. c. Calculate the poverty gap - F1. d. Calculate Atkinson s measure of inequality when the level of aversion to inequality is Consider the following poverty relief program: for every Euro earned by a person the government transfers an additional Euro up until the persons annual earnings are People with earnings between 3000 and 4000 all receive the same as a person with 3000 earnings. Earnings above 4000 reduce the transfers from government at a rate of 0,5 for every earned. a. Construct a graph illustrating this transfer program. What is the critical level of income above which there are zero transfers from government? b. What are the labor supply incentives of the program in its different earnings intervals? c. If we have a uniform discrete income distribution between 1,000 and 50,000 (i.e. 2% people have earnings of 1,000, 2% have earnings of 2,000 2% have earnings of 3,000 and so forth), what is the per capita financial cost of this program (assuming zero incentive effects)?

28 Answers Part B Income Frequency Accumulated % 10% % 25% % 45% % 70% Median Value % 90% % 100% Average =150*0,1+200*0,15+250*0,2+450*0,25+500*0,2+1000*0,1 407,5 a. Poverty line is 50% of median income =450/2 = 225 b. Poverty rate is freq(150)+freq(200)=10%+15%=25% c. Poverty Gap Income Frequency gaps 1-y/PL % 33,333% % 11,111% % 0% % 0% % 0% % 0% GAP=,1*,333+,15*,111+0= 5% d.atkinson with epsilon=2 Income Frequency 1/income % 0,0067 Atk(2)=1-Harmonic Mean/Arithmetic Mean % 0, % 0, % 0, % 0, % 0,0010 =0,1*0,0067+0,15*0,005+0,2*0,004+0,25*0,0022+0,2*2+0,1*0,001 0, harmonic mean=1/0, = 305,6027 Atkinson (2) = 1-305, /407,5= 0,2501

29 14000 Transfer Program Post Transfer Income A B C Gross Income Net Income D a) Up until 3000 we have Gross income = x, transfer = x, post transfer income = 2x. Whem x=3000, post transfer income is This is interval A. From x=3000 to 4000, transfer is 3000, so post transfer income is x+3000 (interval B). From x=4000 to x=10000 transfers are *(x-4000)= x, and post transfer income is x *(x-4000) =0.5 x+5000 (interval C). The critical income level above which transfers are zero is 10,000 (interval D). b) The income effect will always push people to work less. However, the substitution effect will lead people to work more in interval A (higher net wage with 100% subsidy rate), will not operate in areas B and D (unchanged marginal hour net wage), and will lead people to work less in area C (50% implicit marginal tax). c) Gross Income Transfer Per Capita x 2% Total Expense per capita 330