Question:

Macroeconomics problem?

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Consider an economy represented by the following equations:

C=100+0.9Yd;

I=200-500i;

X-F=100-0.12Y-500i;

G=200;

t=0.2;

M=800;P=1;

Lt=0.8Y;

Ls=100-200i (i<0.5)

a) Calculate the equilibrium level of income and interest rate.

b) Find the expression of the aggregate demand. Represent it graphically.

c) What will be the effects on aggregate demand from an increase of 100 m.u. in public expenses?

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  1. It&#039;s simplest statical model.

    X-F should be trade balance ?

    a)

    C=100+0.9(Y-tY)= 100+0.9Y-0.9*0.2Y= 100+0.72Y

    Y=C+I+G+NX=

    =100+0.72Y +200-500i +200 +100-0.12Y-500i=

    =600+0.6Y-1000i

    0.4Y=600-1000i

    Y=1500-2500i

    Since price reaction isn&#039;t given we will assume that economy operates in short-run and price level doesn&#039;t change (P=1=const)

    M/P=Lt+Ls

    800=0.8Y+100-200i (i&lt;0.5 will check this condition later)

    0.8Y=700+200i

    Y=875+250i

    Equilibrium:

    Y=875+250i

    Y=1500-2500i

    875+250i=1500-2500i

    2750i=625

    i≈0.227 = 5/22

    (fits i&lt;0.5 condition)

    Y≈931.82 = 10250/11

    b)

    For all range: { 0 ≤ Y ≤ 1500 } ; { 0.6 ≥ i ≥ 0 }

    For speculative range: { 0 ≤ Y ≤ 250 } ; { 0.6 ≥ i ≥ 0.5 }

    For simple range: { 250 &lt; Y ≤ 1500 } ; { 0.5 &gt; i ≥ 0 }

    800/P=0.8Y+100-200i

    -800/P + 0.8Y +100 = 200i

    i= -4/P + 0.0004Y + 0.5

    Y=1500-2500i = 1500 + 10000/P - Y - 1250 =

    = 250 + 10000/P - Y

    2Y=10000/P + 250

    Y=5000/P + 125

    c)

    Y=600+0.6Y-1000i + 100

    0.4Y=700-1000i

    Y=1750 - 2500i

    i= -4/P + 0.0004Y + 0.5

    Y=500 + 10000/P - Y

    2Y= 500 + 10000/P

    Y=500/2 + 10000/(2P)

    Y=250+5000/P

    Now speculative money - demand condition (i≥0.5)

    Will check a bit later..

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