# Grows at the fixed rate in all periods a set up the

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grows at the fixed rate 𝒛𝒛in all periods. a. Set up the budget constraints of an individual when young and when old in terms of 𝒍𝒍𝒕𝒕(where 𝒍𝒍𝒕𝒕𝒊𝒊denotes a young individual’s supply of labour). Find the lifetime budget constraint of an individual. b. Set up the money market-clearing condition. c. On which island would you prefer to be born? Explain with reference to the rate of return to labour.d. Show how the rate of return to labour and an individual's labour supply depend on the value of 𝒛𝒛For the following parts, assume that the growth rate of the fiat money stock 𝒛𝒛𝒕𝒕is random according to: 𝒛𝒛𝒕𝒕=𝟏𝟏with probability θ, where 0 θ𝒛𝒛𝒕𝒕=𝟑𝟑with probability 1-θ. The realization of 𝒛𝒛𝒕𝒕is kept secret from the young until all puchases of goods have occured (i.e. individuals do not learn 𝑴𝑴𝒕𝒕until period tis over). Given these changes in assumption, answer the following questions: e. How many states of the world would agents be able to observe if information about 𝒊𝒊. 1