MICROECONOMICS II
Problem set II: Partial equilibrium
EXERCISE 1
A) In equilibrium, the quantity demanded coincides with the quantity supplied, so
as demand and supply prices do. Then, in order to get the equilibrium, equate the
∗
∗
∗
10
. It yields that 100
demand and supply functions:
∗
∗
∗
9 . Isolating , we get that
9. Now, introducing the equilibrium quantity
in any of the function (supply or demand) we get the resulting price: ∗ 91.
B) We analyze both plans separately:
Plan A: Subvention to producers of 5€ per bottle sold.
The plan causes that the supply curve shifts to the right. Then, in order to obtain
the new equilibrium, the model would be:
∗
∗
5
Introducing the demand and supply functions we get that:
∗
10 9 ∗ 100
5
∗
Isolating the quantity we get that
9.5. The price that consumers pay is
given by the intersection of the new supply function that is shift to the right and
the demand function. Then, introducing ∗ 9.5 in the demand function we get:
∗
100 9.5 90.5
The Price that consumers will pay will be 90.5. The price that producers get is
obtained introducing the quantity in the old supply function, and we get that:
∗
10 9 ∗ 9.5 95.5
It would be equivalent to obtain it from the new model:
∗
∗
5 90.5 5 95.5
Graphically:
The squared painted with blue lines shows the expenditure made by the State in
the subvention.
Plan B: Discount of 5€ per unit to consumers.
The plan causes that the demand curve shifts to the right. Then, in order to get
the new equilibrium, the model would be:
∗
∗
5
That is, the price that consumers pay is the Price that the producer gets minus 5€
of discount per unit. Introducing the demand and supply functions we get:
∗
10 9 ∗ 5 100
Isolating the quantity we get that ∗ 9.5. The price that consumers pay is
given by the demand function for the new quantity in equilibrium. Then,
introducing ∗ 9.5 in the demand function we get
∗
100 9.5 90.5
The price that consumers pay will be 90.5. The price that producers get is
obtained introducing the quantity in the old supply function, which yields:
∗
10 9 ∗ 9.5 95.5
It would be equivalent to obtain it through the intersection of the supply with the
new demand function.
Graphically:
Paying attention to the 2 new equilibria, we see that both plans are equally
effective, getting exactly the same effects:
- Consumers will pay less, since the Price in both cases will reduce for them
from 91 to 90.5.
- Producers will get more money, since get from 91 to 95.5.
- The quantity in equilibrium rises from 9 to 9.5.
EXERCISE 2
A,B) Firstly, we need to find the supply curve for each of the firms in the industry.
We know that the individual cost function is
43200 3 . From this
function, we can get the marginal cost and the average variable cost:
6
3
We also know that in perfect competition p=MgC.
The individual supply curve is the part of the marginal costs which is above the
average variable costs. In this case, all this part is above, so the individual function
of the supply is:
6
If p=600, in order to determine the quantity produced by each firm of the industry,
simply substitute p in the individual supply function:
600
600
100
6
Representing graphically both functions:
C) If there are 24 identical firms in the industry, the aggregate supply function is
obtained multiplying the individual supply function by 24.
24 ∗ 24
24 ∗
6
4
Graphically, we observe that the slope of the aggregate supply is more pronuntiated
than the individual supply curve:
D) Prices and quantities in equilibrium are determined by the intersection of
aggregate supply and demand curves. Then:
∗
Isolating we get that
∗
4
800 and
∗
∗
19200
3200.
∗
20
∗
E) In order to get how much an individual firm produces, simply divide the total
production by the number of firms in the industry:
3200
∗
133.3
24
In order to obtain profits, multiply the quantity sold by the corresponding price
minus total costs:
∗
∗
800 ∗ 133.3 43200 133.3
∗ ∗
10133.3
F) No. In the long run we are taking into account dynamic aspects of the market,
such as entry and exit of firms. Indeed, in the long run the entry and exit of firms
makes that profits tend to 0. So in that market, we expect that in the long run
firms will enter until profits are exhausted.
EXERCISE 3
A) Quantities and prices in equilibrium are obtained equating demand and supply:
∗
150
2
∗
∗
25
5
∗
Isolating we get that ∗ 17.85 and ∗ 114.3.
We can compute also the surplus of the economy. To do so, firstly represent
graphically the demand and supply functions:
The area with blue lines represent the consumer surplus, while the area with
green lines represent the producer surplus. Computing both areas:
150 114.3 17.85
318.62
2
114.3 25 17.85
797
2
And the total surplus is:
318.62 797 1115.6
B) In order to get the worldly demand and supply, aggregate the national and
internation demands adding quantities as we did in problema set 1. We get then:
0
150
2
150
15
150
3
90
15
2
Now, aggregate the national and international supplies, adding up quantities. We
get that:
15
10
2
25
11
5
25
If we compute the new equilibrium, we get that demand and supply equates
when:
150
15 2
2
And get that ∗ 63 y ∗ 24. Notice that the functions intersect when the
supply is international and the demand is national.
(Hint: in order to know in which parts of the functions the intersection happens,
equate the different parts of the functions among them and obtain the hypothetic
equilibria, until you see the one that fits with the defined functions. For instance,
10
90
, we get that p=21.6.
equating
Then, it does not correspond to the parts of worldly demand and supply
previously specified.)
The effects that we noticed are:
1) The Price falls from 114.3 to 24.
2) Quantity rises from 17 to 63.
3) Only national consumers consume.
4) National producers do not produce, and only international producers do.
We see then that the producer surplus is 0, while the consumer surplus coincides
with the total surplus:
150 24 63
3969
2
I would open the market to the world. Notice that although this measure affects
negatively the producers, consumer’s welfare is so improved that compensates
it.
Graphically:
C) If the produced wine were of a bad quality, we only add the demand and only
consider the national supply (assuming that the wine is so bad that nobody will
buy it). Then, the aggregate supply function coincides with the national one:
25 5
This implies:
25
5
In equilibrium,
150
2
∗
25
∗
5
And isolating we get that ∗ 17.85 and ∗ 114.3. This case coincides with
the case in which the market is closed. The main reason why it happens is due to
the fact that the international demand is willing to buy wine only at low prices.
Then, national producers prefer to sell only to national consumers, getting a
higher surplus. In such a case, we are indifferent about opening or not to the
international markets, mainly because everything remains as in case a (neither
consumers nor producers are affected when they open to the international
markets).
EXERCISE 4
A) The equilibrium price and quantity are computed equating demand and
supply. Then:
∗
5
∗
∗
120
3
∗
Isolating we get that ∗ 15, and introducing the quantity in one of the functions of
demand or supply we get that ∗ 75.
Graphically:
We compute finally the consumer and producer surplus:
120 75 15
337.5
2
75 ∗ 15
562.5
2
b.1) An exogenous reduction in the demand makes that the demand curve shifts
to the left. The main reason is that for each level of prices, consumers are willing
to buy a lower amount of quantity.
Graphically:
We see that when demand falls, price and quantity in equlibrium falls, so as
consumer and producer’s surplus do.
b.2, b.3) If the price of a substitute good rises or consumers have more wealth,
demand shifts to the right. In the first case, it is due to the fact that when the
price of a substitute good rises, demand of this good falls, shifting to the other
good whose price keeps constant. In the second case, when wealth rises,
consumers are willing to buy more quantity of the good for each level of prices
in the market. Graphically:
We see that the price and quantity in equilibrium rises, so as consumer and
producer’s surplus do.
b.4) If production costs rise, the supply curve shifts to the left. This is due to the
fact that, since is more expensive to produce each quantity of the good,
producers will supply every quantity at a higher price. Graphically:
We see that when the supply curve shifts to the left, price will rise while
quantity in equilibrium will fall. In addition to this, consumer and producer
surplus will fall..
Additional exerxises
Exercise 5
Short answer: Suppose that the demand curve is completely vertical and the supply has
a positive slope. In such a case, the tax is supported completely by the consumer,
independently if the tax is charget to the producer or the consumer.
Explanation: The intuition is the following. The demand is totally inelastic. Then,
changes in price will not affect the quantity demanded. We analyze 2 possible cases:
Case 1. Suppose the taxi s charged to the consumer; it would cause that demand shifts
downward. But due to the fact that the demand is vertical, we stay equal. Then, the
consumer will pay the price of the good plus the tax, while the producer will get the
same price. Graphically:
Case 2. Suppose that the tax is charged to the producer. It would cause that the supply
curve shifts to the left, due to the fact that each unity of the good is sold at a price plus
the tax. Due to the fact that the demand is completely inelastic, consumers are willing to
buy the same amount at a higher price, such that the tax is fully supported by the
consumer.
With this exercise we learn that it does not matter if the tax is charged to the
producer or the consumer; who really pays the tax depends on the non/elasticity
of the supply and demand curves.
Exercise 6
Short answer: The national price will rise.
Explanation: In order to answer this question, suppose that the economy is completely
opened. We know that the international supply function of petroleum is completely
.
elastic, with the expression:
Half of the petroleum that the country consumes is imported, and the other half, is
assumed to be of national production. It means that the first unities of petroleum that the
country produces are cheaper than the international ones, while from a certain point on,
they will be more expensive, such that the slope of the national supply function is
positive.
Presumably, the demand of petroleum has a negative slope. Graphically, we could
express our model in this way.
In the graph we see that when the national price is 25 or higher, consumers will only
buy petroleum overseas. (The lines in red represent respectively the demand and the
supply that are given within the country).
Now suppose that the State sets a tax of 5 over imports of petroleum. This fact shifts
upwards the international supply curve, such that internal producers will sell more
petroleum at a higher price, and in the end the national price of petroleum will rise, so
as the national quantity sold does, while the international quantity sold by the rest of the
world and the consumption of petroleum within the country will fall. Graphically:
EXERCISE 7
Short answer: It depends on the price of both pens and the correspondix tax (in case of
having different kinds of supply).
Explanation: Consumers are indifferent about consuming red or blue pens. Then, the
demand of pens is given by:
,
That is, the demand of pens is a function (presumably decreasing) in price of blue and
red pens. But consumers will only buy pens whose price is lower. In addition, the State
has charged a tax over red pens. The supply function of each of the pens would be:
.
.
Then, we observe that in equilibrium:
1) If
, even if red pens are charged with a tax, consumers will
only buy the red ones, since the final price is lower. It would be implied by the
fact that the supply curve of red pens, even with a tax, is to the right from the
supply curve of blue pens.
2) If
, in this case consumers will only buy blue pens, since the
final price is lower than the price of the red ones, which are charged with a tax.
It would be implied by the fact that the supply curve of blue pens is to the right
from the supply curve of red pens.
3) If
, there is a continuum of equilibria in which the consumer
will buy red and blue pens indifferently