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Economic Problem Set 2 - Mexico Household




Question;For problems 1--5 you will use data from the 2008 Mexico National Rural Household Survey to studypoverty in rural Mexico.1 You may assume that the data were generated from a simple random sample inwhich the population of interest is all households in rural Mexico. The household data file called?Mexico Household Data? is available on StartSmite. This data set contains the following variables forthe 1,437 sampled households: ID: The household identifying code. Yi: The household?s income in2007, excluding government transfers. Ti: The amount of income transferred from the government tohousehold i.1. What is your estimate of average household income excluding government transfers for rural Mexicoin 2007? In answering this question, report the following:a. The sample mean,: ______b. The sample variance,: ______c. The variance of the sample mean,: ______d. The standard error of the sample mean,: ______e. The 95% confidence interval of the sample mean, 95% C.I.: _________2. In the year of the survey, the per-capita food poverty line in rural Mexico was 7,596 pesos. Based onthis food poverty line, calculate the poverty headcount index and total poverty gap. For simplicity,assume each household has a single member. Below, report and briefly explain what each one means.a. The Poverty Headcount Index:b. The Total Poverty Gap:Mexico has two main government programs that transfer income to rural households. The first isPROCAMPO, which pays a fixed amount per acre to farmers who grew basic grains prior to the NorthAmerican Free Trade Agreement (NAFTA). The goal of PROCAMPO was to replace pre-NAFTA outputprice supports which were no longer allowed under NAFTA. The second is OPORTUNIDADES, awelfare program that gives payments to poor women provided that their children are enrolled in schoolsand receive health check-ups. Let?s call the households that received some transfers Recipients and thosethat received no transfers Non-Recipients.3. Fill in the table below, where now denotes household income including government transfers.RecipientsNon-Recipients95% C.I.4. What is the difference in income including transfers between recipient and non-recipient households?a. Difference:1 These data were collected jointly by Ed Taylor from UCD and the Colegio de M?xico. In order to reduce costs, the researchers used a stratified random sample in which first villages within each region and then approximately 20 households per village were randomly selected.b. Is this difference statistically significant? How do you know?c. Is this difference economically significant? Briefly support your answer.Can you conclude that the difference in income across the Recipients and Non-Recipients that youfound above was caused by the government?s transfer programs? Briefly discuss why or why not.5. Questions 6 asks you to explore more deeply various measures of income inequality in the context of twohypothetical countries.Consider a society (Society A) in which incomes take values in $1,000 increments between $1,000and $10,000. An equal proportion of the society?s population (10%) occupies each of the ten incomeclasses. In other words, the income distribution for this society is as follows:6. Table 1. Income Distribution in Society AIncome LevelPercent of Population$1000$2000$3000$4000$5000$6000$7000$8000$9000$10000Cumulative percent ofIncomeCumulative Percent ofPopulation10%10%10%10%10%10%10%10%10%10%Fill out the last two columns of Table 1 and show this income distribution as a bar chart or histogram. NOTE: This is NOT the same as a Lorenz curve. Put the income level categories on the horizontal axis and Percent of population in each category on the vertical axis.a. Now consider another society (Society B) in which 50% of the population have incomes equal to $3,000 and the other 50% have incomes equal to $8,000:b. Table 2. Income Distribution in Society BIncome LevelPercent of Population$3000$8000Cumulative percent ofIncomeCumulative Percent ofPopulation50%50%Fill out Table 2 and create the same kind of income distribution diagram that you made in part (a) forthis second economy.c. On a single graph, graph the Lorenz curves for each society (you may want to fill out the cumulativepopulation and cumulative income columns in the charts above before doing this). Which society hasthe more equal distribution by the Lorenz criterion?d. Compute the Gini coefficient and the coefficient of variation for both societies. According to these measures of inequality, in which society is income more equally distributed? Is this consistent with your intuition (Which seems most ?unequal? to you?) In which society might there be a greater awareness of inequality? In which might there be greater scope for social unrest? (Note: there is no single right answer to these questions. The point is to get you to think critically about our measures of inequality in the context of socio-economic polarization. Please explain your thinking carefully.)7. The government of Bolivia is trying to convince GM and Toyota to set up manufacturing plants in LaPaz. Each firm can earn $1 million in profits if they invest $100,000 to set up a plant (the $1 milliontakes the investment into account). In order to satisfy the citizens, the government must charge aprofit tax to any foreign firm operating in Bolivia and redistribute the tax revenues to the people. Ifthe government does not raise sufficient tax revenues, the people will revolt and take over the foreigncompanies. Specifically, if the government raises at least $400,000 in taxes, the people will be happyand not revolt. If the government raises less than $400,000 in taxes, the people will revolt and seizethe factories, causing a loss of $100,000 to any foreign company who chose to invest.So if we let t be the tax rate (i.e., t =.1 means a 10% tax rate) and be the company?s profit, thepayoffs to each foreign company are as follows:? If a company invests and the people do not revolt, its payoff is.? If a company invests and the people revolt, its payoff -$100,000.? Finally, if a company does not invest its payoff is 0.a. Show that multiple equilibria will exist if the government of Bolivia charges a 30% profit tax on foreign firms. To do so, fill out the payoff matrix in Table 7a below and identify the equilibria.Table 7a. Payoffs to firms under 30% profit taxToyotaInvestNot InvestInvestGMNot Investb. Show that only a single equilibrium will exist if the government of Bolivia instead charges a 70% profit tax on foreign firms. To do so, fill out the payoff matrix in Table 7b below and identify the equilibrium.Table 7b. Payoffs to firms under 70% profit taxToyotaInvestNot InvestInvestGMNot Investc.Why are there multiple equilibria in the first case but not the second case? (Hint: is there a complementarity?)


Paper#56177 | Written in 18-Jul-2015

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