Download Exam 11th Febraury 2005: Solution

Exam 11th Febraury 2005: Solution
1.

A) Agree
In general terms, we can define the PPF as a measure of cost.
Then the absolute value of the slope is the opportunity cost of
producing one more unit.

Resources are scarce and more adequate for producing some
certain goods than others, so, the more of one thing is being
produced, the highest will be the opportunity cost of producing
one more unit.

Any production has an opportunity cost, to produce more of one
good, society must pass resources from the production of
others goods.
B) Agree
Concept of elasticity and revenue.
We define revenue as the product of price times quantity.
R  px x
Graphically, revenue is the shaded rectangular area shown in the
following figure
px
5
x
When the price changes, revenue will change. But see that this
change (whether it is small, large or even negative) will depend on
the slope of the demand curve, and therefore on the elasticity.
To analyse this relationship it is convenient to get acquainted with a
very useful transformation of the above equation. It turns out that a
product in levels is equivalent to a sum in rates of change.
R px x


R
px
x
Or, expressing these rates of change in percentages, we have
%R  %px  %x
The percentage change in revenue is equal to the percentage change
in the price plus the percentage change in the quantity demanded.
Now, this expression enables us to say what happens to revenue
knowing only the percentage change in price and the elasticity.
For instance, suppose that we are told that in this market the price
has decreased by 10% and that the demand elasticity (in absolute
terms) is 2. What is the percentage change of revenue?
The reasoning is as follows: If the absolute value of the demand
elasticity is 2, then the ratio of the percentage change in the quantity
demanded to the percentage change in the price is –2
%x
 2
%px
From this we can find out what the percentage change in the quantity
demanded is; namely:
%x  2(%px )
Since we know that the price has decreased by 10%, it is immediate
to find out that the quantity demanded has increased by 20%
%x  2(10)  20
Then applying these data to the revenue formula above we have:
%R  10  20  10
Conclusion: If the price goes down by 10% and the demand elasticity
is 2, revenue will increase by 10%.
Why is this happening? Look again at the revenue formula
%R  %px  %x .
This last statement, in bold, is enough to answer question b), all
previous paragraphs are written to properly introduce the point.
The price and the quantity demanded will always move in
opposite directions. The demand elasticity gives us precisely
the extent of this negative relationship. If the demand is
elastic (greater than 1) the positive percentage change of the
quantity demanded will be larger than the negative
percentage change of the price, and therefore the percentage
change in revenue will be positive (the positive effect of the
quantity on revenue will dominate the negative effect of the
price).
C) Agree
We define the benefit, in fact it can be defined in two ways:
1)  = TR – TC
2)  = (P – ATC) Q
Where  = benefit, TC = total cost, TR = total revenue, P = price,
ATC = average total cost, Q = quantity.
1) TR = P Q
Given the information we have, we know that Q = 10- P, from here
we can get P, such as P = 10 – Q, then
TR = (10 – Q) Q, multiplying, TR = 10Q – Q2
In order to get the equilibrium price and quantity, we ought to figure
it out, so:
In equilibrium: MR = MC
Additionally we know that TC = 4Q + 4
From TC and TR we obtain, just with the derivative of the two
functions MC and MR:
MC = 4
MR = 10 – 2Q
Equating both expressions, 4 = 10 -2Q, from here we get Q = 3 and
substituting in demand function, P = 7.
Substituting, the value of Q in TC, TC = 16, and doing identically in
TR, then TR = 21, so:
 = 21 – 16, benefit equal to 5.
According to procedure 2, we should first obtain ATC, we know that
ATC = TC/Q, that is, (4Q + 4)/3 = 4/3 + 4
Than benefit will be = [7 – (4+4/3)]3 = 21 – 16 = 5
2.A) Profit maximization output
We have three characteristics of competitive markets:
a) Many buyers and sellers; they do not influence prices. They are
price takers.
b) Goods and services offered are all the same.
c) Firms can freely enter or exit the market.
In competitive markets, both average and marginal revenue equal
price. AR is obvious. MR is trickier. If the price is constant, by how
much a seller will increase its revenue when it raises its quantity sold
by one unit? Answer: By the price of this unit.
So, conclusion:
AR = MR = P
Then, in competitive markets, since MR=p, we have that the rule for
maximizing profits can be stated like this: the profit maximizing
output is that one for which p=MC; firms should produce output up to
the point at which marginal cost equals price.
B)
Free entry and exit of firms from the market is one of the
characteristics of competitive markets. To see what are the reasons
why a firm may want to exit or remain in the market we have to
introduce two definitions:
Shutdown: Refers to a short run decision not to produce anything
during a specific period of time because of adverse market conditions.
Exit: Refers to a long run decision to leave the market for good.
These are different decisions because in the short run firms still have
to pay for fixed costs. If a firm decides to suspend temporarily its
activity because prices are momentarily low, it has to keep incurring
in its fixed expenses. Not so in the long run. If the firm decides to
stop producing for ever it can sell, the firm will save these fixed costs.
The firm’s short run decision is to shut down. Suppose a particular
firm that decides to shut down because the price of services has gone
down and decides to suspend services until the price recovers. It still
keeps fixed costs but saves variable costs. On the other hand it
looses the revenue. It will shut down if the profit from doing so is
greater that the profit from remaining in the market.
Shut down if p < AVC
The firm’s long run decision to exit:
Suppose you become convinced that the price of the product you
produce is not going to recover and consider the decision to exit the
market for good. Then you can sell your firm and therefore need not
incur in fixed costs. The decision is then,
Exit if p < ATC
General conclusions:
a) If the firm produces anything, it produces a Q at which MR=MC
(p=MC). Yet if at that quantity p<AVC, the firm is better off shutting
down and not producing anything.
b) A firm considering exit from the market will consider p, if price falls
below average total cost, the firm is better off exiting from the
market.
3.Xd =6 – 4px +0.005m + 2py
Information: py = 0.5, m = 3000, pI = 3
Xs =7 + 4px - 3pI
A)
Substituting the values in both functions, we get:
Xd = 6 – 4px +15 + 1
Xs = 7 + 4px - 9
from these equations, Xd = 22 – 4px
Xs = -2 + 4px
When Xd = 0, then px = 5.5
When Xs = 0, then px = ½
In equilibrium Xd = Xs , that is, 22 – 4px = -2 + 4px and we get
px = 3 and Xd = Xs = 10
B)
Increases py , now py = 2
Xd = 6 – 4px +15 + 2x2, then ,
Xd = 25 – 4px
Xs = -2 + 4px
When Xd = 0, px = 6.25
In equilibrium Xd = Xs
25 – 4px = - 2 + 4px
Equilibrium price = 3.38, equilibrium quantity = 11.5
C)
Consumer surplus =
(bxh)/2
b= 5x5-3 =2.5
h = 10
(10x2.5)/2 = 12.5 (grey shaded area)
B= 3 -1/2 = 2.5
Producer surplus = (b.h)/2
H = 10
= (2.5 x 10 )/2 = 12.5 (yellow shaded area)
Total surplus = consumer surplus + producer surplus = 12.5 + 12.5
= 25
P* new price = 4, we compute again with this new price Xd and Xs
Xd = 25 – 4px
Xs = -2 + 4px
Xd = 25 – 4x4 = 6
Xs = -2 + 4x4 = 14, Excess supply = 14 – 6 = 8
If the quantity supplied is 14, at what price? In the demand function
for a quantity of 14, look for the price
14 = 22 - 4px , px = 2
New consumer surplus =
(bxh)/2
b= 6
h = 5.5 – 4 = 1.5
= (6x1.5)/2 = 4.5 (red shaded area)
New producer surplus= triangle’s area + rectangle’s area
[(2 -1/2)x6]/2 = 4.5 +rectangle’s area
rectangle’s area = bxh =
b=6
h = 4 -2 = 2
6x2 = 12, producer surplus = 12 + 4.5 = 16.6 (yellow shaded area)
Total new surplus = 16.5 + 4.5 = 21
Old surplus = 25
Deadweight loss = New surplus- old one = 21 – 25 = -4, blue shaded
area.
(b x h)/2
This area will be:
h = 4 -2 = 2
b = 10 - 6 = 4
the area will be = (2x4)/2 = 4
The efficiency cost generated by the imposition of this regulated price
is 4. They don’t suffer the same, consumers are worse off than
before, their surplus is now 4.5, and before it was 12.5, whereas
producers have improved, now they get a surplus of 16.5, when they
had 12.5.
4.A) Disagree
Information from the question:
Labour force participation = 60%
Unemployment rate = 10%
Adult population = 50 million
Question: number of unemployed is 2 million?
Solution: Labour force participation/ population = 0.6, as population
is 50 million, then: Labour force participation/ 50 = 0.6
Labour force participation = 30 million (active population)
Unemployment rate= Unemployed/Active population,
0.10 = unemployed/30, unemployed = 3 million.
B) Disagree
MV =PY, V is considered constant, we can express
%M = %P + %Y, according to the information: %M = 52%,
%P=32%
That mean that y has increased by 20%
C) Disagree
It is just the other way around, a modern economy is characterized
by its financial system. The more modern an economy is, the most
sophisticated its financial system.
5.The amount of money the banking system generates with the
reserves is called the money multiplier. We can express the financial
position of the first bank, assuming it has 1000€ in deposits, and all
deposits are held as reserves, its situation will be:
Suppose the 1st bank decides to keep 10% of its deposits in reserve
and to loan out the rest, the new T-account:
Now, the bank has two kinds of assets: it has 100€ of reserves and
its loan of 900€. We consider the money supply, currency plus
demand deposits, it will be 1900€, thus when banks hold only a
fraction of deposits in reserve, banks create money. We assume now,
that the 1st bank uses the 900€ to buy something from someone who
deposits the currency in a 2nd bank. The T-account for the 2nd bank:
Second Bank
The process goes on and on. Each time money is deposited and a
bank loan is made, more money is created.
The money eventually created in the economy is:
Original deposit
= 1000€
1st bank lending
= 900€ = [.9x1000]
nd
2 bank lending
= 810€ = [.9x900 ]
rd
3 bank lending
= 729€ = [.9x810 ]
………… and so on
……………….
Total money supply . . . . . . . . 10.000€
The process the money creation can continue forever. In this
economy, where the 1000€ of reserves generates 10000€ of money,
the money multiplier is 10. The money multiplier is the reciprocal of
the reserve ratio. If R is the reserve ratio and is equal to 1/10, then
the money multiplier is 10.
The tools that the monetary authorities can use to control the money
supply are:
1. Open-market operations
2. Reserve requirements
3. Discount rate
1. when it buys or sells bonds, to increase the money supply it
buy bonds from the public, the euros it pays for the bonds
increases the number of euros on circulation, and the opposite,
to reduce the money supply.
2. Regulations on the minimum amount of reserves that banks
must hold against deposits. An increase in the reserve
requirements, raises this values and lowers the money
multiplier and the money supply.
3. Discount rate: is the interest rate on the loans that the FED
makes to banks. A higher rate of discount discourages banks
from borrowing reserves from the FED and reduces the quantity
of reserves in the banking system, which in turns reduces the
money supply.
6.A) Given Y  C (Y  T )  G  I (r )
The left hand side of the equation is the total income that remains
after paying for consumption minus the taxes over it and government
purchases, and it is called, the national saving of the economy,
denoted by S, then.
S  I (r )
Thus, the left hand side of the equation is the supply for loanable
funds, because this supply comes from the people who have extra
income and they want to save and lend out, i.e. saving is the source
of the supply of loanable funds. Interest rate balances the supply and
demand for loanable funds.
The demand is the right hand side of the equation and comes from
households and firms that want to borrow to make investment. That
is, investment is the source of the demand for loanable funds.
The demand curve for loanable funds, depends on interest rate.
B)
The point where supply and demand intersect, give us the interest
rate, and at this interest rate the quantity of loanable funds supplied
is equal to the quantity of loanable funds demanded.
The supply, as it is fixed, does not depend on interest rate.
C) i) If there is an increase in the amount of capital available in
the economy, we can think that there is a budget surplus which
contributes to increase the supply of loanable funds, and that will
provoke:
• interes rate will decrease from r1 to r0
Investment will increase from I1 to I0

Broadly speaking, an increase in the supply of loanable funds,
reduces the interest rate, stimulates investment. Higher investment,
in turn, means greater capital accumulation and more rapid economic
growth, and eventually more income.
ii) An



increase in G:
Increases interest rate, from r0 to r1
Decreases investment from I0 to I1
Crowding out total
iii)If G increases and T increases, the increase in G will be greater
than the decrease in consumption because the effect of taxes via
marginal propensity. There will be a partial crowding out effect.
There is an increase in interest rate and a decrease in investment.