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- 3. Suppose that we have a Solow model with one twist. The twist is that thereis a government. Each period, the government consumes a fraction of output,sG. Hence, the aggregate resource constraint is:Yt = Ct + It + Gt.Where Gt = sGYt. Define private output as Ypt = Yt − Gt. Suppose thatinvestment is a constant fraction, s, of private output (consumption is then1 − s times private output). Otherwise the model is the same as in the text.104(a) Re-derive the central equation of the Solow model under this setup.(b) Suppose that the economy initially sits in a steady state. Suppose thatthere is an increase in sG that is expected to last forever. Graphicallyanalyze how this will affect the steady state value of the capital stockper worker. Plot out a graph showing how the capital stock per workerwill be affected in a dynamic sensePlease no written by hand Suppose that in a country one-third of all females born die in infancy, one-third of all females die in infancy, one-third die at age 30, and one-third live to age 60. Women bear one child at age 25, one child at 28, one child at age 32, and one child at age 35. One-half of children are girls. b.) Suppose the mortality is reduced so that there is no infant mortality. Half of all women die at age 30 and a half at age 60. Compute the NRR.Julie lives for two periods. She works in the first, saves some of her income, and retires inthe second and lives off her savings. For every coconut she saves today, she earns an interestrate of r = 2%. Julie’s generation comprises of 1,000 people and each generation grows byn% relative to the previous one.a. In the first period Julie saves 100 coconuts for retirement. How many coconuts will shehave when she retires?b. Now suppose that the government implements a pay-as-you-go social security system,forcing every person in Julie’s generation to pay 100 coconuts to a social security fund thatwill distribute the money to the currently old. In exchange, when Julie retires each youngperson will pay 100 coconuts to the social security fund, and the revenue will be dividedequally among the future retirees. How much will be the revenue of the social securitysystem, and how many coconuts will each retiree will receive?c. What will have to be the range of values for n so that the government’s…
- Suppose that the current (first) generation consists of 1 million people, half of whom are women. Assume the total fertility rate is 1.2 and the only way people die is of old age. Instructions: In part a, enter your answer as a whole number. In parts b and c, round your answers to 2 decimal places. a. How big will the fourth generation (the great-grandchildren) be? ___ people b. How much smaller (in percentage terms) is each generation than the previous generation? ___ percent c. How much smaller (in percentage terms) is the fourth generation than the first generation? ___ percentConsider an overlapping generations model. Suppose population grows at a 2% rate, and wage grows at a 6% rate. Generation 2 has 500 people, who have an average salary of $30,000, and everyone pays 8% of their income to generation 1. What is the total amount generation 2 pays to generation 1? If generation 3 pays generation 2 the same dollar amount gen-eration 2 paid generation 1, what percentage of their income dothey pay?Suppose that the current (fifi rst) generation consists of 1 million people, half of whom are women. If the total fertility rate is 1.3 and the only way people die is of old age, how big will the fourth generation (the great-grandchildren) be? How much smaller (in percentage terms) is each generation than the previous generation? How much smaller (in percentage terms) is the fourth generation than the fifirst generation? Are you surprised by how quickly the population declines?
- How do we use these FOCs to show that (wtNt)/Yt =(1-α) if Yt = At Ktα Nt1-αAssume there are two countries: South Korea and the United States. South Korea grows at 4 and the United States grows at 1. For the sake of simplicity, assume they both start from the same fictional income level, 10,000. What will the incomes of the United States and South Korea he in 20 years? By how many multiples will each countrys income grow in 20 years?The market research department at a manufacturing plant determines that 30% of the people who purchase the plant's product during any month will not purchase it the next month. On the other hand, 40% of the people who do not purchase the product during any month will purchase it the next month. In a population of 1000 people, 200 people purchased the product this month. How many will purchase the product next month and in 2 months? (a) next month___?___ people (b) in 2 months __?___ people
- TFR and Birth Rates:a. Define the crude birth-rate and the total fertility rateSuppose country A and B have are identical in their population size andstructure, and rate of mortality, but A has a higher average TFR than B.b. What could be some of the reasons why A has a higher fertility ratethan B?c. What will be true about the size and age structure of the population in Arelative to B in 25 years? Will the proportion of young people to oldpeople be higher or lower in A?d. Now suppose the governments of both A and B impose a one-child policy(the TFR was greater than 1 in both A and B). Suppose the policy is fullyenforced (i.e. all families indeed have one kid). Is the fertility rate thesame in A and B? Is the birth rate same in A and B?e. Is the population growth rate higher or lower in A?f. As more time passes, the population growth will eventually slow down inboth countries. What will happen to the proportion of old in the populationas population growth slows down?True or false (explanation needed) 2. The Gini coefficient of global incomeinequality (based on the distribution ofincome per-capita) will be higher if weconvert income per-capita to acommon currency using the officialexchange rate compared to thepurchasing power parity exchange rate.Consider a closed economy without government; resource constraint is Y = C Production is (FIRST IMAGE SHOWN) K = 400 Consumer preferences is U (C,I) = ln (C) + ln (I) a) Suppose that z = 10. Show that if the consumerís time endowment is given by h = 6000 hours, the equilibrium quantity of leisure is 2 3 h = 4000 hours. What is the real wage? (b) Suppose that z = 20. Show that the equilibrium quantity of leisure is still 2 3 h = 4000 hours. What is the real wage? (c) Comparing parts (a) and (b), what can you infer about the income and substitution e§ects of a productivity increase?