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KEY Practice problem #2 for econ 304 final exam - fall 2016
Suppose the economy is characterized as follows:
MP:
r = r(bar) + λ π
SRAS: π= πe + 1 ( Y - Y P) + p
Potential GDP: YP = 10, πe = 2%, λ = .2, r(bar) = 1, p =0
a) Derive an expression for the IS curve....Y in terms of r
Y = [ 3 + 1 -.2 + 1.9 + 1.5 - 1.5] x (1 / 1 - .5) - (.1 + .2 + .2)/(1 - .5) r
Y = 11.4 - r
b) Derive an expression for Aggregate Demand
AD: Y = 11.4 - [ 1 + .2 π)........AD: Y= 10.4 - .2π
c) Find the value of GDP
Y= 10.4 - .2 [2 + 1( Y - 10) + 0]
Y(1 + .2) = 10 + 2
Y = 12 / (1 + .2)......Y = 10
d) What is the GDP gap?
THERE IS NONE - ACTUAL = POTENTIAL = 10!
e) Find the values of π and r
π = 2% + 1[10 - 10] + 0 ......= 2% = π
r = 1 + .2(2) .......r = 1.4%
DRAW THREE DIAGRAMS - AN MP CURVE DIAGRAM TOP LEFT, AN 'IS'
CURVE DIAGRAM ON TOP RIGHT, AND A AS/AD DIAGRAM BELOW THE 'IS'
CURVE. PLEASE BE SURE TO COMPLETELY LABEL DIAGRAMS - LABEL
THESE INITIAL CONDITIONS AS POINT A ON ALL THREE DIAGRAMS.
Suppose we have a positive price shock - an adverse supply shock like in the 1970s = oil
shock so that p = 5 (p was originally 0). Potential GDP (YP) falls to 9 (was 10). All else
remains constant including AD.
f) Resolve for the new level of output, Y, π, and r and label on all three diagrams as
point(s) B.
Y= 10.4 - .2 [2 + 1( Y - 9) + 5]
Y(1 + .2) = 10 + 1.8 - 1
Y = 10.8 / (1 + .2)......Y = 9
π = 2 + 1(9 - 9) + 5
π=7
r = 1 + .2(7).......r = 2.4
g) Using a production function diagram (on top) and labor market diagram (on bottom),
show the movement from A to B. Be sure to completely label diagrams.
h) Explain the movement from A to B in your labor market diagram... why does the level
of labor input change?
i) Why does output change? Name two reasons.
j) Policy makers are not happy with these results (unemployment has risen!) and decide
to use expansionary policy to get the economy back to the original output as in part c)
above. To do so, the government increases G to by .6 trillion so that the new G = 2.5
Trillion (old G was 1.9). All else remains constant - resolve for Y, π, and r and label as
points C on all 3 diagrams.
NEW IS CURVE
Y = [ 3 + 1 -.2 + 2.5 + 1.5 - 1.5] x (1 / 1 - .5) - (.1 + .2 + .2)/(1 - .5) r
IS: Y = 12.6 - r
NEW AD
Y = 12.6 - (1 + .2π).........AD: Y = 11.6 - .2π
Y = 11.6 - .2[2 + 1( Y - 9) + 5]
Y(1 + .2) = 11.6 - .4 + 1.8 - 1
Y = 10
π = 2 + 1 (10 - 9) + 5...........π = 8
r = 1 + .2(8).........r = 2.6
k) We know that points C are not consistent with the long run given that potential GDP =
9 which does not equal actual GDP at point C. Explain how the economy will return to
long run equilibrium and what determines the speed in which the economy would return
to long run equilibrium. What would be the equilibrium inflation rate (π) in the long run?