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    Ye Chen BScUniversity of Bristol

    Application: Ph.D in Economics State University of Pennsylvania

    Supplementary Material: Writing Sample

    International Economics Tutorial Class Paper

    (October, 2009)

    Question:

    In early 2009 the US initiated a sharp expansion of fiscal policy.

    Explain the likely effects on US aggregate demand, the value of the

    US dollar, and the size of its current account deficit of such a fiscal

    expansion.

    In February 2009, the US congress passed the $787 billion worth economic stimulus

    package --- American Recovery and Reinvestment Act of 2009. By building

    necessary models, this essay is to discuss the likely effects of the large fiscal

    expansion has on several key factors of the US economy including aggregate demand,

    the value of the US dollar, and the size of the current account deficit.

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    Aggregate demand (D) is the amount of a countrys goods and services demanded by

    households and firms throughout the world. A countrys overall short-run output level

    depends on the aggregate demand for its products. For an open economys, the

    aggregate demand is the sum of consumption demand (C), investment demand (I),

    government demand (G), and the net export demand, that is, the current account (CA).

    The relationship is expressed as:

    D = C + I + G + CA

    To determine how aggregate demand (D) changes when other factors of the economy

    increase or decrease, we need to look into elements which influence the four types of

    demand, or correspondingly, the four types of expenditure.

    Consumption expenditure depends on disposable income, Yd (which equals national

    income less taxes, Y-T). It can be written as: C = C(Y-T). The impact of increase in Yd

    on consumption (C) is positive, as we know that more disposable income lead people

    to spend more.

    We assume that investment (I) and government expenditure (G) are given.

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    The exchange rate (E) between two currencies specifies how much one currency is

    worth in terms of the other. It is the value of a foreign nations currency in terms of

    the home nations currency.

    The current account balance (CA), viewed as the demand for a countrys exports less

    that countrys own demand for imports, is determined by two main factors: the

    domestic disposable income (Yd=Y-T) and the real exchange rate(EP/P), where E is

    the nominal exchange rate, Pis the foreign price level, and P is the home price level.

    So, CA = CA(EP/P, Yd)

    An increase in real exchange rate (EP /P) means an depreciation of domestic

    currency. It makes domestic goods and services cheaper relative to foreign goods and

    services, which shifts both domestic and foreign spending from foreign goods to

    domestic goods. As a result, exports (EX) rises and imports (IM) decreases. Therefore

    the domestic countrys current account (CA) will rise. An appreciation of domestic

    currency, on the other hand, will worsen the current account.

    An increase in Yd causes domestic consumers to spend more on all goods, including

    imports from abroad. But Yd has no influence on exports because it does not affect

    foreign consumers. So a rise in Yd worsens the current account (CA).

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    Combining the four components, we can write the aggregate demand equation as:

    D = C(Y-T) +I + G + CA(EP/P, Y-T)

    From this expression, we can see that a rise in the government spend G will increase

    the aggregate demand (D). So, the expansionary fiscal policy of the US government at

    the beginning of the year (the Stimulus Package) which includes huge amount of tax

    relief, investment in infrastructure, etc, will boost the aggregate demand of the US

    economy in the process of the gradual recovery from the recession.

    Too analyze the impact of the Stimulus Package on the US dollar exchange rate and

    furthermore, the current account balance, it is convenient and important for us to

    establish the diagrammatic model of AA-DD schedules.

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    Aggregate DemandOutput YAggregate demandD

    45Y1D1

    The graph below shows the relationship between aggregate demand (D) and real

    income Y for fixed values of the real exchange rate, taxes, investment demand, and

    1

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    government spending. As Y rises, consumption rises by a fraction of the increase in

    income, which explains that the slope of the aggregate demand curve is smaller than

    1.

    Equilibrium in output market requires domestic output Y to be equal to the aggregate

    demand D. This is indicated by point 1, where the aggregate demand curve intersects

    the 45 degree line.

    Now we can look at how the exchange rate and output are simultaneously determined.

    D=YAggregate DemandE2

    Aggregate demand

    Rise in exchange rate, E1to E2

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    45

    Aggregate Demand

    Y1 Output YY2

    Exchange Rate

    E

    DD

    1

    2

    E2

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    The above two graphs illustrate the relationship between the exchange rate and output

    implied by output market equilibrium. With fixed price levels at home and abroad, the

    rise in the nominal exchange rate (E1 to E2) makes domestic goods and services

    cheaper relative to foreign goods and services. So the demand for domestic products

    is now higher and the export will increase. However, although the amount of foreign

    goods demanded by domestic consumers will decrease (volume effect), each amount

    of foreign goods becomes dearer so it will cost more in terms of domestic currency

    (value effect). Here we assume the volume effect is greater than the value effect and

    the import decreases (Marshall Lerner Condition). The change in the exchange rate

    (E1 to E2) shifts the aggregate demand curve upward. And the equilibrium output

    level rises from Y1 to Y2. This explains the upward-sloping DD curve.

    If we assume P and P are fixed in the short run, a depreciation of the domestic

    currency (a rise in E, or E1 to E2) is associated with a rise in domestic output (Y1 to

    Output YY1 Y2

    E1

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    Y2), while an appreciation (a fall in E) is associated with a fall in domestic output.

    This is the DD schedule shown in the lower graph (previous page).

    We have derived DD schedule using the analysis of equilibrium in output market.

    Now let us look at the equilibrium in the asset market.

    The interest parity condition tells us that the foreign exchange market is in

    equilibrium when assets or deposits of all currencies offer the same expected rate of

    return when measured in terms of a common currency. This is captured in the

    equation : R = R+ (Ee E)/E

    where R is the interest rate on domestic currency deposits and Ris the interest rate

    on foreign currency deposits. E is the spot exchange rate and Ee is the expected future

    exchange rate.

    The interest parity condition indicates a downward-sloping curve in the foreign

    exchange market, i.e. a negative relationship between R and E, given Rand Eeare

    constant. The intuition behind this is that when the domestic interest rate (R) rises, the

    demand for the domestic currency will increase because it offers a higher interest.

    This higher demand will drive the price of the domestic currency up and the

    exchange rate (E) down.

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    In the domestic money market, the condition for equilibrium is that the supply of

    money equals the demand of money, i.e. Md = MS. This is captured in the equation:

    Md/P = L(R, Y)

    Where Md/P is the real money supply and L(R, Y) is the real money demand. The

    impact of R on the value of L(R, Y) is negative because a rise in the interest rate R

    makes interest-bearing non-money assets more attractive and thus lowers real money

    demand L(R, Y). A rise in output Y, increases real money demand L(R, Y) by raising

    the volume of monetary transactions people need.

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    Money Demand Curve,

    L(R, Y)

    Real domestic money holdings0Exchange Rate

    E

    Foreign

    Exchange

    Market

    Domestic

    Money

    Market

    Domestic

    Interest Rate,

    R

    Domestic-currency

    return on foreign-

    currency deposits

    Real

    Money

    Supply

    E1R11

    Now if we combine our analysis of foreign exchange market and the domestic money

    market, we can picture the asset market equilibrium in the diagram below (next page).

    MSP

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    The graph above captures the analysis of domestic money market and the foreign

    exchange market. The upper part of the graph indicates the relationship between

    domestic interest rate R and the exchange rate E. The lower part of the graph indicates

    the relationship between the domestic interest rate R and the real domestic money

    holdings. The equilibrium of domestic money market (Md = MS) leads to point 1

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    where the money demand curve intersects the real money supply line. The interest

    rate R1 clears the domestic money market while the exchange rate E1 clears the

    foreign exchange market.

    In the graph below (on the next page), a rise in output from Y1 to Y2 raises aggregate

    real money demand from L(R, Y1) to L(R, Y2). For each level of interest rate people

    now demand more money holdings and this shifts the money demand curve

    rightwards to a new position. This new equilibrium in the domestic money market

    gives a higher domestic interest rate, R2. And as the domestic interest rate rises to R2,

    the foreign exchange market will correspondingly see the change in exchange rate

    from E1 to E2, which indicates an appreciation of the domestic currency.

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    2Real domestic money holdings0Exchange Rate

    E

    Foreign

    Exchange

    Market

    Domestic

    Money

    Market

    Domestic

    Interest Rate,

    R

    Domestic-currency

    return on foreign-

    currency deposits

    Real

    Money

    Supply

    E1R11Output risesR2E2L(R, Y1)L(R, Y2)MS

    P

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    Therefore, for given values of MS, P, Rand Ee, equilibrium in asset market requires

    that a rise in domestic output (Y) must be accompanied by an appreciation of the

    domestic currency. This relationship between output (Y) and exchange rate (E) is the

    AA schedule. AA schedule can be captured by a downward sloping curve on the

    following graph.

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    Exchange rate, EOutput, YAADDE1Y1

    Now that we have derived DD schedule based on equilibrium in the output market

    and AA schedule based on equilibrium in the asset market, we can look at the short-

    run equilibrium of the economy as a whole by combining the two equilibria.

    Assuming again the domestic output prices are fixed in the short run, we can put AA-

    DD schedules on the same graph below, where the intersection (point 1) indicates the

    output market equilibrium and asset market equilibrium simultaneously.

    1

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    Going back to our initial discussion of the effects of the US government expansionary

    fiscal policy, we can use the established AA-DD schedules model to analyze them.

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    Exchange RateEOutput YY1Y2DD11E0DD2Y1Output YY2Aggregate demandD

    Government spending

    rises

    D=Y( US StimulusPackage )

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    This fiscal expansion shifts the DD schedule to the right (DD1 to DD2).

    In the short run, peoples expectation on the exchange rate (Ee) does not change, and

    in our discussion we mainly focus on fiscal expansion so we assume there is no

    monetary policy movement (MS does not change). AA schedule therefore does not

    move in the short run following the fiscal expansion. The graph below shows the shift

    of DD schedule from DD1 to DD2. The exchange rate then falls from E1 to E2, which

    means the US dollar will appreciate.

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    AAUS Stimulus

    Package

    Exchange rate, EOutput, YDD1E1Y1DD2E2Y2

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    Based on the model, in the short run, as a result of the fiscal expansion the US dollar

    should appreciate in value, which makes foreign goods and services cheaper, and this,

    along with an income rise (Y1 to Y2), should increase imports. Exports on the other

    hand, will suffer a decrease as the US goods become more expensive following a

    dollar appreciation. The two effects will worsen the US current account. The

    expansionary fiscal policy will therefore, reduce the US current account balance in the

    short run.

    In the long run, people observe the drop in the exchange rate and their expectation

    (Ee) changes as well. As the expected exchange rate goes down, AA schedule will

    shift downward. At the same time, the output will be adjusted to the long run natural

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    Exchange rate, EOutput, YAA1DD1E1YnDD2AA2E2E3123

    level (Yn), which is the level of output that can be sustained over the long term due to

    natural and institutional constraints. The economy reaches its new long run

    equilibrium at point 3 in the graph on the next page.

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    In the long run, the US dollar will appreciate even more than the short run (E1 to E3).

    This will further worsen the US current account deficit. But the aggregate demand

    comes back to the long run natural level (Yn

    ). This can be explained as that in the

    long run, the effect of the fiscal expansion on the output level is completely offset by

    the worsened current account caused by the US dollar appreciation.

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    Whether this US stimulus package is a long run fiscal expansion is arguable. Some

    say it is only a temporary policy because of the financial crisis while others believe it

    has permanent effects to the US economy. The fact that the US dollar has actually

    depreciated since the Congress passed the stimulus package might suggest that our

    model does not quite fit the current real world situation. It is therefore important to

    point out that although the discussion in our model focuses on the theoretical analysis

    of the fiscal expansion, there are other factors in the current situation which can also

    seriously influence the US aggregate demand, the value of the US dollar and the size

    of the US current account deficit, e.g. monetary policies such as cutting interest rates,

    US domestic inflation, etc.

    However, the essay question indicates that the discussion should be in the direction of

    fiscal expansion.

    References:

    [International Economics] Theory and Policy, Seventh Edition. Paul R. Krugman &

    Maurice Obstfeld, 2006. Pearson Addison Wesley.

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    Flexible Exchange Rates in the Short Run, Rudiger Dornbusch & Paul Krugman.

    [Brookings Papers on Economic Activity 1976] Arthur M.Okun and George L.Perry,

    Editors. The Brookings Institution, Washington DC.