QUESTIONS :

The initial population is 1000 and population grows by 10% every year. The initial stock of money is 200 and money grows by 20% each year. The probability that a person is on Island 1 is 1/3 and the probability that the person is in Island 2 is 2/3. The labour supply function is given by:

l (pⁱ_t) = 4+ 0.25pⁱ_t where notations have usual meanings.

(a)Solve for using the market clearing condition.

(b)Can the worker make use of this price level as an indicator of the unknown monetary policy?

(c)How can the workers make use of the price obtained in part a to decide on their work decision?

Additional Information :

LG structure, with people living in two separate islands (this is also known as the \Lucas-Islands" model). Assumptions:

?Total population across islands is constant (Nt=N).

?Half of the old population lives in each island. Their randomly distributed in the islands, independently from where they lived while young.

?The young are distributed unequally : 2/3 live in one island.

?In any single period, each island has an equal chance of having the larger share of young. The chance (or probability) is serially uncorrelated (e.g. like a fair coin toss).

?Fiat money stock evolves as: Mt=zM_t-1

?Increases in the stock of money are introduce w/ lump-sum transfers to the old: at=[1(1/z_t)](v_tM_t/N)

Informational assumptions are critical:

?In any period, the young cannot see neither the number of young people in the island(s) nor the size of the subsidies to the old.

?The stock of at money is known with 1-period delay.

?The price of goods in each island is known only to people in that island.

? No communication between the islands is possible within a single period.

Although there are important variables the individuals cannot observe directly, we don't assume they are stupid/irrational. They are assumed to know the possible outcomes they face and the probabilities of each. They are free to infer whatever they can from the price they observe.

= Rational Expectations

-> interpretation of our OLG model:

?y: young's time endowment (i.e. units of time).

?Time endowment can be used for leisure (c1, non-market good) or labor (l).

?The young work to produce goods to sell to the old.

?Let l_tⁱ =l(pⁱ_t) be the labor of a young individual in period t for a given price of goods, pⁱ_t, on island i .

?1 unit of labor produces 1 unit of output (so that l(pⁱ_t) also represents output).

With these changes, the B.C. of the young is:

c¹_1,t + lⁱ_t = cⁱ_1,t + vⁱ_t mⁱ_t = y(1)

- BC of the young: cit + / = ci.+ + vimt = y (2) A young's money holdings (vim; ) is equal to the amount of goods the young produces and sells to the old (1;), so It = move. The BC of the old, in period t + 1 is: (2 + +1 = vitIm+ + at+1 = t41 4+ + at+1 = Pt Pt+ 1 It + at+1 (3) - Note: second period consumption depends on the island the indiv. was born (i), and on the island j were it is randomly assigned when old.r i_ r r i_ CLt'l'lt CLt'l'Vtmt }" U _ 1 1" _ C2,t+1 \"lam: 'l' 3t+1 [ !- People choose i: to maximize expected utility. given a local price pg. I pifpi+1 2 rate of return to labor. I We'll assume that an increase in the current price of goods. other things equal. will induce the young to work more. (if you've taken intermediate/advance micro } substitution effect dominates wealth effect)