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Pontificia Universidad Católica de Chile
Instituto de Economía
Segundo Semestre 2017
Ayudantía 1
Macroeconomía II
Caio Machado
Ayudantes:
Cristóbal Ojeda: ctojeda@uc.cl
Sofia Gillet: msgillet@uc.cl
A Parable of Macroeconomics: Formal Model
Suppose there are two farmers, i 2 b, g, who are each able to produce x̄ sacks of beef and grain each per week
respectively. They also both hold money, mi, and represent their preferences with
Ui =
X
j2b,g
ln(xji ) + �ln(
mi
p
)
where xji represents farmer i’s consumption of good j, and p is the overall price level, p =
1
2
P
j2b,j
pj .
The farmer’s budget constraints will be:
m0 + x
i
jp
i = mi + x
j
ip
j
So, the demand function can be written as:
x
j
i =
mi
�p
j
=
x
i
jp
j +m0
(1 + �)pj
Money Supply
Central Bank offers money and have two goals:
1. Money stability
2. Normal functioning of external and internal payments
Central Bank can change the money supply by three ways:
1. Open market operations (QE)
2. Short run operations (REPO)
3. Exchange operations
• Banking reserve
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Money multiplier
Think in the following close economy, where there is no currency and the money it is only deposits. A representative
commercial bank assign credits (C) at rate ic in a market where the demand is infinitely elastic. Also, it face an
deposit supply that is infinitely elastic and pays a rate id and receives deposits for D.
The commercial bank cannot fix his reserves R bigger than R̄, fixed by the central bank. The commercial bank
maximizes the following benefits choosing credits, deposits and reserves.
⇧ = Cic �Did
looking at the reserve coefficient as restriction, the commercial bank should take into account that:
R � ✓D
and the fact his passive and assets are equal in equilibrium:
D = R+ C
1. By substitution, show that the commercial bank problem can be written as the following:
Maximize
⇧ = C(ic � id)�Rid (1)
subject to the reserve coefficient
R � ✓
1� ✓C (2)
and the fact reserves cannot be bigger than the restriction fixed by the central bank:
R  R̄ (3)
2. From the equation (1) in the previous answer, graph iso benefit curves in a space (R,C). On this graph,
represent the restrictions given by the equations (2) y (3), making the following assumption:
(1� ✓)ic > id (4)
Which is de combination of C and R that maximize the benefit of the bank? Mark this point on the graph
and call it A.
3. The equation (4) must be fulfilled so the commercial bank fix positives quantities of D, C and R in equilibrium.
Give the intuition behind this condition.
4. Estimate the equilibrium monetary base and deposits. Deduce the money multiplier.
5. Explain why an increase in the monetary base (from an open market operation for example) result in a bigger
increase of the deposits in this economy.
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Money Demand
Baumol Tobin model
1. Suppose a simple Baumol-Tobin model where a consumer spend his income linearly and makes nequal with-
drawals of R, and minimize the opportunity cost ( iY2n ) of keeping money. The cost of a withdrawal is Z, in a
context where the money is necessary to go shopping.
(a) Set the cost minimization problem and clearly identify the trade-off between alternative use and linear
fix costs.
(b) Which is the most important conclusion of this model and which are the core assumptions? Which is
the intuition of the fix cost of withdrawals?
(c) How would be affected the demand for real money balances with an increase in the number of banks
where they can make a withdrawal?
(d) (Proposed) Suppose that there is a new way to make transactions, through electronic discounts T, where
0  T  Y , and T is the total resources discounted in the period. This system is used by all business
and it does not discount the money from the current account until the moment of the transaction, so
it does not represent an opportunity cost. How the money demand is affected in this case if the use of
T has a cost ⌧ for each discounted cent? What conditions is needed to have a money demand in this
economy?
Cash in Advance Model, infinite horizon
1. Consider a close economy, where a representative agent must choose the consumption and asset trend, such
that maximize:
1X
i=0
�
i
U(Ct+i)
where 0  �  1 , and the utility function is strictly increasing, concave and differentiable, where the
maximization is subject to a sequence of budgetary constraints, as to cash in advance.
(a) Show the optimization problem and find the FOC of Ct, Mt+1, Bt+1,Kt+1.
Quantitative Theory
As you all should know, this theory tell us about a relationship between money supply, velocity of money, prices
and real product. More specifically:
MV = PY
differentiating we can rewrite this as:
µ = ⇡ + g
(Proposed) True or false and why
1. If the potential real growth rate is 3%, velocity of money is constant at 2% and the Central Bank prints every
period at constant 5% rate, so the quantitative theory suggest that inflation will be 0% each period.
2. The purchase and sale of foreign currency in exchange of domestic currency from de Central Bank is commonly
known as open market operations.
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3. An increase on the price level suggest that the economy is growing and the aggregate demand is increasing.
4. According to Baumol-Tobin model, an economy with high poverty and inequality, we will have agents who
keep more money as percentage of their income than others.
5. Discuss the function and characteristics of money. Today, bitcoins have irrupted as a new kind of money.
Does it fulfill with this characteristics? What effect would have this new kind of money?
(Proposed) Money Demand
The money demand of an economy is defined as:
log(
M
P
) = 0, 8log8Y )� o, 5log(i)
1. Estimate the growth of money necessary to reduce the interest rate in 1% and you expect that real product
growth 4%, keeping the price level constant.
2. Suppose now that goverment is willing to accept a 5% inflation. Repeat question 1.
3. The GDP growth at 5% anually, inflation end up being 10% and the central bank has increased the money in
8%. What happened with the interest rate?
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