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International Macroeconomics

Consider a small open economy that lives for two periods, only, (t and t + 1; for
all purposes to some extent if it makes it easier you can think of this as t =
0 and t = 1) and is inhabited by a continuum of identical individuals grouped into an
aggregate risk-sharing household. Each period aggregate output Yt
is produced via the
function Yt = ZtLt where Zt
is exogenous productivity and Lt
is labor. If output is not
consumed or loaned out in any one period, then it spoils and cannot be carried over to
the following period (this just means that the economy cannot save internally, itís only way
to save would be to make international loans). This is a small open economy, so it can
borrow and lend freely at the constant-across-periods international interest rate r. The
householdís instantaneous utility is given by Ct=Lt and the household discounts the future
at rate , where: 2 (0; 1) is the householdís (constant) subjective discount factor (i.e.,
0 < < 1, where 2 means ìbelongsî and is the Greek letter ìbetaî); C is consumption;
L is labor. Moreover, the household ìownsî the production function, so its thinking with
regards to its maximization problem is akin to that of a benevolent social planner. Now,
consider the following version of the householdís intertemporal utility maximization problem,
where A denotes the (endogenous) state variable ì(internationally traded) assets.î The
household chooses consumption, labor, and assets to maximize lifetime utility (hint: this
involves Ps=t+1
s=t
, for all purposes, as noted earlier, to some extent if it makes it
easier you can broadly think of this as t = 0 and t = 1; the explicit changes just
involve setting up certain things using s instead of our usual t, but at the end of
the day things should look entirely familiar: trust me!) such that
Cs + As+1 (1 + r) As + ZsLs
Let s denote the time-s Lagrange multiplier.

  1. (Worth 15 points.) State the householdís Lagrangian.
  2. (Worth 35 points.) State the Örst order conditions for the householdís (that is, the
    economyís) utility maximization problem using s = t.
  3. (Worth 50 points.) Is the following claim true, false, or uncertain? When the
    economy is open, if =
    1
    1+r
    , then the solution to the householdís period-t intertemporal
    1
    utility maximization problem implies that Ct+1 =
    Zt+1
    Zt
    Ct
    . (Note: again, if it is
    easier to think about this, you can just imagine that t = 0, in which case
    the question is asking whether it is true C1 =
    Z1
    Z0
    C0:) Justify your answer with
    thorough mathematical detail. (Huge hint: There are three ways through which Ct+1,
    Ct, Zt+1, and Zt can meet in this problem. The Örst way is really straightforward and
    involves combining two FOCs. The second will be revealed by going through our “usual
    thing” in the small open economy case, which is equating the slope of an indi§erence
    curve with the slope of the lieftime budget constraint. Iím not saying that equating the
    slope is the solution, Iím saying that in going through these steps youíll see the second
    instance in which all of these variables meet. The last is a potential combination
    between the Örst and second ways. Thatís it, you do those three things and they are
    exhaustive to be able to answer the claim.)

Sample Solution

War Poems The principal sonnet of war verse was a sonnet composed by Walt Whitman before 1900 years. It is classified "originated from the field father." This sonnet tells the family how heard the news that his child was harmed in fight. At first, it clarifies that his sister gets a letter and asks her dad and mom. At that point the writer will keep on clarifying the setting of the ranch and its experience. "The apple of the plantation is ready and the grapes of grapes will be grapes." "The sky is extremely quiet ...", it is peaceful and quiet and wonderful. "He made a calm and delightful spot. WB Yeats' first fight melody was "Mentioned to give war verse" on February 6, 1915. Because of the solicitation of Henry James, Yeats composed a political sonnet about World War I. Yeat changed the title of the sonnet to "Give a companion". On 20 August 1915, Yeat composed a letter to Coul Park's Curry and requested that an unbiased nation sign his affirmation. Purpose behind quietness "When it was reproduced later, the title was changed to" Requested to give war verse ". Yeats' most well known war verse is "Ireland's pilot anticipates his demise." This sonnet is a monolog given by the pilot in the First World War, and the talker depicts his looming passing. This sonnet is about the job of Irish officers who battled with Britain when Ireland attempted to set up freedom. The principal sonnet mirrors the picture of war that the vast majority know well. This sonnet "Flanders Battlefield" is presumably the most well known and mainstream war sonnet. It was first distributed in British 'punch' magazine in December 1915. Very quickly, this sonnet represents the penance of all the battle in World War I. "Flanders Battlefield" was made by a specialist and educator of Canada, John McCrea who worked in the South African War and the First World War. He was moved to the clinical group and doled out to a French emergency clinic. He was dynamic in 1918 and passed on of pneumonia. His sonnet assortment "Flanders Field" and other verse assortments were distributed in 1919. This sonnet is still piece of a commemoration in Canada and different nations. Maybe the most acclaimed contemporary use of this sentence is the title of the sonnet "Dulce et Decorum est" by British writer Wilfred Owen during the First World War. Owen's verse depicts the gas assault during the First World War and is one of his numerous enemy of war sonnets that were not declared until the finish of the war. In the last barely any lines of this sonnet, Horatian phrases are communicated as "antiquated untruths". Individuals accept and utilize the first of that sonnet to clarify that Owen is attempting to deride the sonnet by Jessie Pope (who commended the war and selected in a straightforward devoted verse). "Little accomplice" who is eager about charging and shooting. Like "telephone"
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