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.
Graphically, revenue is the shaded rectangular area shown in the following figure
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.
Or, expressing these rates of change in percentages, we have
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
From this we can find out what the percentage change in the quantity demanded is; namely:
Since we know that the price has decreased by 10%, it is immediate to find out that the quantity demanded has increased by 20%
Then applying these data to the revenue formula above we have:
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
.
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) P = TR – TC
2) P = (P – ATC) Q
Where P = 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:
P = 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 from these equations, Xd = 22 – 4px
Xs = -2 + 4px
Xs = 7 + 4px - 9
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 = b= 5x5-3 =2.5
(bxh)/2 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 = b= 6
(bxh)/2 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
%DM = %DP + %DY, according to the information: %DM = 52%, %DP=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]
2nd bank lending = 810€ = [.9x900 ]
3rd 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
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.