Download Econ202 Sp14 answers 1 2 3 4 5 6 to midterm exam group B

Student No._______________________
Name____________________________
KOÇ UNIVERSITY
ECON 202 / SPRING 2014
MIDTERM EXAM / GROUP B
April 20th
CLOSED BOOK AND NOTES
ANSWER ALL QUESTIONS
SHOW YOUR REASONING
TOTAL TIME: 120 MINUTES
Question (1)
Question (2)
Question (3)
Question (4)
Question (5)
Question (6)
Question (1) Consider an economy in which
(1) people and firms hold 1 TL of currency for every 10 TL they hold in deposits,
(2) the required reserve ratio is 9%, but
(3) banks find it safer (and prefer) to hold 6% of deposits as excess reserves.
Suppose that the Central Bank keeps total reserves constant at 450 TL (by conducting day-to-day
open market operations). Answer the following questions:
(a) Calculate the total amount of money held in deposits.
(b) Calculate the total amount of currency held by non-bank public.
(c) Calculate the money supply.
(d) Calculate the monetary base.
(e) Calculate the money multiplier in two different ways.
(f) Suppose people and firms change the way they split their money holdings between currency and
deposits so that they now hold 1 TL of currency for every 4 TL they hold in deposits. The Central
Bank provides more currency if necessary, but still keeps total reserves at 450 TL. Recalculate all
your answers in parts (a) – (e).
(g) Does the money supply increase or decrease with fixed reserves as the way people split their
money into currency and deposits changes as above? Why?
Answer
(each yellow box is worth 1 point)
(a) Total Reserves = Required reserves + Excess reserves
= 0.09 Deposits + 0.06 Deposits = 0.15 Deposits
D = R / 0.15 = 450 / 0.15 = 3000
(b) Currency ratio = 1 / 10 = 0.1
Currency = Currency ratio x Deposits = 0.1 x 3000 = 300
(c) Money supply = Currency + Deposits = 300 + 3000 = 3300
(d) Monetary base = Currency + Reserves = 300 + 450 = 750
(e) Money multiplier = M / B = 3300 / 750 = 4.4
or Money multiplier = (c + 1) / (c + r) = (0.1 + 1) / (0.1 + 0.15) = 1.1 / 0.25 = 4.4
(f) Since banks' reserve holdings per unit deposits do not change, reserve ratio = 0.15
D = R / 0.15 = 450 / 0.15 = 3000
Currency ratio is changed: c = 1 / 4 = 0.25
Currency = Currency ratio x Deposits = 0.25 x 3000 = 750
Money supply = Currency + Deposits = 750 + 3000 = 3750
Monetary base = Currency + Reserves = 750 + 450 = 1200
Money multiplier = M / B = 3750 / 1200 = 3.125
or Money multiplier = (c + 1) / (c + r) = (0.25 + 1) / (0.25 + 0.15) = 1.25 / 0.40 = 3.125
(g) The money supply increases because, as currency ratio decreases, money multiplier decreases,
but the Central Bank increases monetary base buy providing currency even though it keeps reserves
the same.
Points:
(a) 2 points
(b) 2 points
(c) 1 points
(d) 1 points
(e) 2 points
(f) 7 points
(g) 3 points
Total = 18 points
Question (2) Consider the following model for the loanable funds market in a closed economy in
the long run with the properties given in (1) – (4) below.
(1) Consumption expenditures (C) depend positively on current disposable income (Y – T) and
negatively on the real interest rate (r), and MPC = 0.6.
(2) Investment expenditures (I) depend negatively on the real interest rate (r).
(3) The government determines its purchases of goods and services (G) and the total amount of taxes
(T).
(4) The long run real GDP (YLR) is constant over time.
Suppose that the government increases its purchases of goods and services by 360 units, and 75% of
this increase is financed by raising current taxes and the rest by new government borrowing, without
people anticipating any increases in future taxes due to this new borrowing.
(a) What is the change in current taxes equal to?
(b) What is the change in current disposable income equal to?
(c) What is the change in consumption expenditures equal to?
(d) What is the change in national saving equal to? By how much does the saving curve shift (in the
horizontal direction)?
(e) How do the real interest rate and equilibrium investment change?
(f) What can you say about the magnitude of the change in equilibrium investment?
(g) Draw a diagram displaying the S and I curves, indicate the equilibria before and after the change in
G in the loanable funds market, and show as many of your results in the above parts as possible on this
diagram.
Answer
(each yellow box is worth 1 point)
(a) ΔT = 0.75 x ΔG = 0.75 x 360 = 270
T increases by 270 units
(b) Δ(disposable income) = ΔY – ΔT = 0 – 270 = –270
units
disposable income decreases by 270
(c) ΔC = MPC Δ(disposable income) = MPC (ΔY – ΔT) = 0.6 x (–270) = –162
Consumption decreases by 162 units
(d) ΔS = ΔY – ΔC – ΔG = 0 – (–162) –360 = –198
Saving decreases by 198 units at any r
(which means that S curve shifts left or in by 198 units in the horizontal direction)
(e) Since S curve shifts left but I curve stays the same,
equilibrium real interest rate increases and equilibrium investment decreases
(f) Investment decreases by less than 198 units
because S curve is positively sloped (and not vertical) and that is because C depends negatively on r.
(g) (see next page)
The diagram must include:
Saving (S) and Investment (I) measured along the horizontal axis and real interest rate (r)
measured along the vertical axis,
Initial S curve (positively sloped),
I curve (negatively sloped),
New S curve to the left of the initial S curve,
Horizontal shift in the S curve = 198 units.
Real interest rate and investment in the initial equilibrium indicated, and
Real interest rate and investment in the new equilibrium indicated.
r
S2
S1
eq r2
eq r1
I
198 units
eq I2 eq I1
Points:
(a) 2 points
(b) 2 points
(c) 2 points
(d) 3 points
(e) 3 points
(f) 2 points
(g) 6 points
Total = 20 points
S, I
Question (3) Consider the following model for the money market in a closed economy for the short
run with the properties given in (1) – (3) below.
(1) The real amount of money demanded (MD / P) depends negatively on the nominal interest rate (i),
positively on the real GDP (Y), and positively on the total wealth (Ω) held by people.
(2) The nominal amount of money supplied (MS) (or, nominal money supply for short) is determined
by the Central Bank of the country which conducts day-to-day open market operations to keep MS at
the level it targets.
(3) People do not change their expectations about the inflation rate (so π is constant).
Suppose that the money market is initially in equilibrium. Then the Central Bank increases the
nominal amount of money supplied.
(a) Draw a diagram displaying demand and supply of money, and indicate the initial equilibrium in the
money market as well as the effect of the increase in the nominal amount of money supplied. (By how
much do demand or supply of money curves shift?)
(b) How is the new equilibrium reached (that is, what variable changes and by how much) ?
(c) Fill in the blanks in the table below by indicating if each variable listed is exogenous or
endogenous.
variable
exogenous or endogenous
variable
MD
MS
MD / P
P
i
MS / P
Y
π
Ω
r (real interest
rate)
exogenous or endogenous
Answer (each yellow box is worth 1 point)
(a) The demand for real money curve stays the same
because real GDP (Y) and wealth (Ω) do not change.
The supply of real money shifts right because the nominal amount of money supplied is increased.
It is not possible to say anything about the magnitude of the shift because we are not given the
increase in M,
but, if M changes by ΔM, the horizontal shift in the supply of real money will be equal to ΔM / P.
The diagram must include:
Real amount of money M / P along the horizontal axis and nominal interest rate i along the vertical
axis
The initial supply of real money (vertical) at M1 / P1
The initial demand for real money curve (negatively sloped)
The initial equilibrium nominal interest rate i1 at the intersection of initial demand and supply
The new supply of real money (vertical) at M2 / P1 to the right of the initial supply
Horizontal shift in the supply of real money = ΔM / P
The new equilibrium nominal interest rate i2 at the intersection of the initial demand and the new
supply curves
i
M1 / P1
M2 / P1
ΔM / P
i1
A
i2
B
mD
M/P
In the diagram, M1 / P1 is the initial real amount of money supplied, and M2 / P2 is the real
amount of money supplied after the nominal amount of money supplied has been increased.
Also, mD denotes the demand for real money function at the given levels of real GDP and
wealth. A and B are the initial and new money market equilibria, respectively.
(b) The new equilibrium is reached by a decrease in the nominal interest rate since the amount of real
money supplied increases above the amount of real money demanded at the initial i.
But since we do not given the elasticity of real money demanded to the nominal interest rate,
we can not say anything about how much the nominal interest rate will fall.
(c)
variable
exogenous or endogenous
variable
exogenous or endogenous
MD
endogenous
MS
exogenous
MD / P
endogenous
P
exogenous
i
endogenous
MS / P
exogenous
Y
exogenous
π
exogenous
Ω
exogenous
r (real interest
rate)
endogenous
Points:
(a) 10 points
(b) 2 points
(c) 10 points
Total = 22 points
Question (4) Consider the loanable funds market in a closed economy in the long run. You are
given that
(1) Consumption expenditures (C) depend positively on disposable income (Y – T) and negatively on
the real interest rate (r), such that if disposable income increases by one unit, consumption increases
by less than one unit (MPC). Consumption depends also expected future disposable income.
(2) Investment expenditures (I) depend negatively on the real interest rate (r) and positively on the
expected future profitability of investments.
(3) The government determines the government purchases of goods and services (G) and the total
amount of taxes (or the tax revenue) (T).
(4) The long run real GDP (YLR) is constant over time.
Suppose that the loanable funds market is initially in equilibrium. Then an increase in consumer
confidence raises consumers' expectations about their future income and, at the same time, firms begin
to expect higher future profitability of investments.
(a) Draw a diagram displaying national saving (S) and I, and indicate the initial equilibrium in the
loanable funds market as well as the effect of the changes in consumer confidence and firms'
expectations. (How, if at all, do S or I curves shift?)
(b) How is the new equilibrium reached (that is, what variable changes) ? How do equilibrium values
of r, S, and I change?
Answer
(each yellow box is worth 1 point)
(a) The increase in consumer confidence that raises consumers' expectations about their future income
causes
current consumption expenditures C to increase and saving S to decrease at any r.
So, S curve shifts left.
As firms begin to expect higher future profitability of investments,
they increase their investment expenditures I at any r. So, I curve shifts right.
The diagram must include:
Saving (S) and Investment (I) measured along the horizontal axis and real interest rate (r)
measured along the vertical axis,
Initial S curve (positively sloped),
Initial I curve (negatively sloped),
New S curve to the left of the initial S curve,
New I curve to the right of the initial I curve.
Real interest rate and investment (or saving) in the initial equilibrium indicated, and
Real interest rate and investment (or saving) in the new equilibrium indicated.
(see next page)
r
S2
S1
eq r2
eq r1
I1
eq I2 eq I1
I2
S, I
(b) Since we consider the economy in the long run,
Y will be constant at its long run value along both S curves. Therefore, the equilibrium can not be
reached by a change in Y that would shift the S curve again, so that the new equilibrium will be
reached by a change in the real interest rate.
As S and I curves shift, both of them will cause the equilibrium r to increase.
Therefore, the real interest rate will have increased unambiguously in the new equilibrium.
But the shift in S curve causes the equilibrium values of S and I to decrease
whereas the shift in I curve causes them to increase
(that is because C depends on r negatively and S curve is positively sloped).
Therefore, the equilibrium values of S and I can decrease, increase, or stay the same,
depending on the relative magnitude of shifts in S and I curves.
Points:
(a) 11 points
(b) 11 points
Total = 22 points
Question (5) Consider a small open economy with perfect capital mobility in which consumption
expenditures (C) depend positively on disposable income (Y – T) and negatively on the real interest
rate (r). The economy is in the long run and has a trade deficit. Suppose that the government begins
to subsidize investment by instituting an investment tax credit (while adjusting other taxes to hold its
tax revenue constant). (Note: An investment tax credit is a reduction in a firm's income tax when it
buys new capital goods.) As it turns out, one of the results of this investment tax credit in this country
is that the firms begin to buy more machinery and equipment from abroad. Drawing the necessary
diagrams for the loanable funds market as well as the foreign exchange market (and using the usual
notation r, r*, S, I, NX, and ε for domestic real interest rate, world real interest rate, national saving,
investment, net exports, and real exchange rate, respectively) in the long run, explain and determine
(a) how S changes at any r,
(b) how I changes at any r,
(c) how the equilibrium r, S, and I change,
(d) how NX changes at any ε,
(e) how the equilibrium ε and NX change.
Answer
(each yellow box is worth 1 point)
(a) Since total tax revenue T does not change and Y is constant at the long run real GDP level,
C at any r does not change, and so S at any r does not change (S curve does not shift).
(b) As the investment tax credit makes it possible for the firms to buy the same amount of investment
goods at lower prices in effect, investment expenditure will increase at any r (I curve shifts out or
right).
(c) Since the economy is a small open economy with perfect capital mobility, the domestic real
interest rate r stays constant at the world real interest rate r*.
Consequently, equilibrium S stays the same but equilibrium I increases from I1 to I2 (see the first
diagram below). Since the economy has a trade deficit already, or S – I1 < 0, the trade deficit grows
(the gap between S and I increases), so S – I2 < 0 and the absolute value of S – I2 is larger than the
absolute value of S – I1.
Diagram for the loanable funds market
The diagram must include:
Saving (S) and Investment (I) measured along the horizontal axis and the (domestic) real interest
rate (r) measured along the vertical axis,
Initial S curve (positively sloped),
Initial I curve (negatively sloped),
New I curve to the right of the initial I curve,
Real interest rate equal to the world real interest rate r* where r* is below the intersection point
between initial S and I curves so that S at r* is less than I at r*
equilibrium S indicated (which is at r*),
initial equilibrium I indicated (which is also at r*),
new equilibrium I indicated (which is also at r*) to the right of the initial equilibrium I,
r
S
r*
initial I
eq S
eq I1
eq I2
new I
S, I
(d) As firms increase their investment expenditures and begin to buy machinery and equipment from
abroad, imports increase at any ε (because the increase in imports is not a result of any change in ε).
So, since higher imports mean lower NX, NX at any ε decreases (NX curve shifts left or in).
(e) In the initial equilibrium, NX1 = S – I1, and since the economy has a trade deficit initially, NX1 is
negative at the initial equilibrium real exchange rate ε1 (see the second diagram below). After the
changes in S – I and NX curve, the new equilibrium will be at ε2, with equilibrium NX being
NX2 = S – I2, and now NX is still negative with larger absolute value (or, trade deficit grows, or
simply, NX decreases).
Diagram for the foreign exchange market
The diagram must include:
NX and S – I measured along the horizontal axis and real exchange rate ε measured along the
vertical axis
Initial S – I curve (vertical)
Initial NX curve (negatively sloped)
Initial equilibrium real exchange rate ε and initial equilibrium NX indicated
New S – I curve to the left of the initial S – I curve
New NX curve to the left of the initial NX curve
New equilibrium real exchange ε rate and new equilibrium NX indicated
ε
S – I2
S – I1
ε2
ε1
new NX initial NX
NX2
<0
NX1
<0
NCF, NX
If NX shifts left as much as S – I, equilibrium ε will not change (or stay at ε1).
This happens if the entire increase in I due to investment tax credit is spent on imported investment
goods (at the initial real exchange rate).
Alternatively, if NX shifts left less than S – I, equilibrium ε will increase (for example, to ε2 in the
second diagram below). But this can happen only if part of the increase in I is spent on imported
investment goods and the remaining part on domestically produced investment goods (at the initial
real exchange rate).
IMPORTANT NOTE (that you do NOT need to remember during the midterm exam):
In the entire answer above, a big simplification is used by implicitly assuming that increased
investment expenditure does not lead to faster accumulation of physical capital which would make the
long run real GDP larger instead of remaining constant.
Points:
(a) 3 points
(b) (points given to the answers in the diagram)
(c ) (points given to the answers in the diagram)
Diagram for the loanable funds market: 7 points
(d) 1 point
(e) (together with the diagram for the foreign exchange market) 9 points
Total = 20 points
Question (6) Use the model of the small open economy with perfect capital mobility in which
consumption expenditures (C) depend positively on disposable income (Y – T) and negatively on the
real interest rate (r) to predict what would happen to the trade balance, the real exchange rate, and the
nominal exchange rate in response to the event that the Central Bank doubles the money supply in the
long run.
Answer
(each yellow box is worth 1 point)
Consider first the effects of the increased nominal supply of money in the loanable funds market as
well as the foreign exchange market.
In the loanable funds market,
S at any r will stay the same (or, S curve will not shift).
I at any r will stay the same (or, I curve will not shift).
The world real interest rate r* will not change.
Since the domestic real interest rate r is determined by (or, is equal to) the world real interest rate,
r will not change either.
Consequently, the equilibrium gap between S and I (or, S – I) will not change.
In the foreign exchange market,
As the last conclusion above implies, S – I will stay at a constant value (determined in the loanable
funds market) independent of the real exchange rate ε (or, S – I curve which is vertical will not shift).
Net exports (NX) will not be affected (or, NX curve will not shift).
As a result of these, the equilibrium real exchange rate ε will not change
and the equilibrium quantity of net exports (or, the trade balance) will not change either.
Now consider the effects on the money market:
The increase in the money supply will affect the price level and there will be some inflation but
after the full effect of the increase in money supply on the price level is realized in the long run, there
will not be further inflation expected thereafter and the expected inflation π will return to its previous
value, so we can take π as constant.
The fact that the real interest r is also constant implies together with a constant π
that the nonimal interest rate i is also constant because i ≈ r + π (or, because of Fisher equation).
Notice that, since we are considering the economy in the long run,
the real GDP in the long run is not affected by the money supply either.
As the nominal interest i and the real GDP in the long run are not affected,
velocity V will not be affected either.
(ALTERNATIVE ANSWER: The last 5 points can be given to the following answer:
If we accept that the classical theory holds according to which real variables are not affected by the
changes in the nominal supply of money in the long run, velocity will be not affected.)
Consider now the equation of exchange: M V = P Y.
A constant velocity and a constant real GDP level Y imply together with the equation of exchange
that the price level P is proportional to the amount of nominal money supplied M.
(ALTERNATIVE ANSWER: The last 3 points can be given to the following answer:
As the nominal interest i and the real GDP in the long run are not affected,
demand for real money MD / P = L (i, Y) will not be affected either.
Consider now the money market equilibrium: M / P = L(i, Y)
or, real supply of money M / P equals the real demand for money L(i, Y).
A constant real demand for money implies together with the money market equilibrium that the
price level P is proportional to the amount of nominal money supplied M.)
Therefore, price level P doubles in the long run as the money supply is doubled.
We can finally turn to what happens to the nominal exchange rate:
Consider now the relationship between the real exchange rate ε and nominal exchange rate e:
ε = (e x P) / P* or ε x P* = e x P where P is the domestic price level and P* is the foreign price
level.
As we found out when we considered above the foreign exchange market, the real exchange rate is
not affected. The doubling of nominal money supply in a small economy can not be expected to affect
the foreign price level, either. Therefore, e x P must be constant, which implies that
the nominal exchange rate decreases (in fact, to one half) (or, the domestic currency depreciates) as the
nominal money supply is doubled.
Points:
Loanable funds market: 5 points
Foreign exchange market: 4 points
Money market: 8 points
Nominal exchange rate: 3 points
Total = 20 points