The table below shows the probability that a mother in a given part of the income distribution (given by the row) will have a daughter in a given part of the income distribution (given by the column). So, for example, the daughter of a women with the income in the bottom third of the income distribution will herself have a 60% chance of being in the bottom third, a 25% chance of being in the middle third, and a 15% chance of being in the top third.
What is the probability that the granddaughter (along the maternal line) of a woman in the middle third of the income distribution will herself be in the middle third of the income distribution? (Hint: note that a woman in the second generation does not necessarily have to be in the middle third of the income distribution, so you need to take into account 3 cases: when the mother of the granddaughter is the top, in the middle, and in the bottom thirds of the income distribution.)
2. This problem tests your understanding of the effect of the income distribution on savings rates.
The economy of Sonrisa has 1000 people in three income categories: poor, middle class, and rich. The poor ear $500 per year and have tE?5?end it all to meet their consumption needs. The middle class earn $2,000 per year, of which $1,500 is spent and the rest saved. The rich earn $10,000 per year, and consume 80% of it, saving the rest.
(a) Calculate the overall saving rate in Sonrisa if 20% of the people are poor and 50% are in the middle class.
(b) Suppose that all growth occurs by moving people from the poor category to the middle-class category (all poor people become middle-class people). Will the saving rate rise over time or fall?
(c) Answer part (b) using another growth scenario, where growth changes over time in a way opposite to that in (b): all middle-class people become poor.
Income Group of Daughter
Income Group of Mother Bottom third Middle third Top third
Bottom third 0.6 0.25 0.15
Middle third 0.25 0.5 0.25
Top third 0.15 0.25 0.6