1.Assume that rural wage is $1000/month wage in the formal urban sector is $1800

1.Assume that rural wage is $1000/month wage in the formal urban sector is $1800/month and wage in the informal sector is $500/month. Calculate PF (the probability of obtaining a job in the formal sector) and PI (the probability of obtaining a job in the informal sector) under which NO more rural-urban migration would occur. Assume no unemployment. You can round your answers to 2 decimal places.2.In some LDCs families maximize total family income. Total family income is the summation of the income obtained by family members working in the city and the income obtained by those who remain in the farm:Total family Income = Expected Urban Income + Rural IncomeA given family farm would produce each month according to the following schedule (valued in monetary terms): TOTAL OUTPUT ($) 1 person 30002 people 50003 people 65004 people 7800 5 people 8500 6 people 9100The formal urban sector pays $1200/month whereas the informal sector pays $300/month. Assume that PF and PI are the same that you calculated in the previous exercise. How many members of this family will migrate to the city?3.A farm in an LDC with 5 adult members has the following output schedule:Number of Workers 1 2 3 4 5 Output ($) 1000 1800 2400 2800 3000Output is distributed equally among the members of the family. Assume that a job in the city pays $1300. However there is an unemployment rate of 50% (wage under unemployment is $0). Assume no informal sector. a.Assume that each member of the family acts selfishly. Under these circumstances those who migrate to the city act on their own (they do not receive any income from the farm nor they send any urban income to the farm). Those who remain in the farm will share the farm production equally. Given these assumptions how many people will migrate to the city?b.Now assume that the family is altruistic: they work either in the city or the farm and then the total family income is pooled and shared equally. How many people will migrate to the city? 4.The Malthusian explanation of the demographic dynamics supposes that an increase in per capita GDP leads to an increase in population. Recent experience however suggests that this is not the case. In fact increase in income has been associated with a decrease in the fertility rate. Explain.5.Summarize in your own words the theory of the demand for children. Explain how the reduction of gender discrimination in LDCs may induce a reduction in the fertility rates.