Respuesta :
Answer:
a. The equilibrium price is 4 and the equilibrium quantity is 12 units.
The producer surplus is 12, the consumer surplus is 18 units, and the total economic surplus is 30.
b. At the world price of $3, the quantity demanded will 16 units and the domestic quantity supplied will be 6 units. The quantity imported will be 10 units.
3. The producer surplus is 3, the consumer surplus is 32 units, and the total economic surplus is 35.
The total surplus is higher after the trade, this implies that the country is better off.
Explanation:
The demand equation is given as:
Qd = 28 - 4P
The supply equation is given as:
Qs = -12 + 6P
At equilibrium, the quantity demanded is equal to quantity supplied.
Qd = Qs
28 -4P = -12 + 6P
28 + 12 = 6P + 4P
40 = 10P
P = 4
Putting the value of P in demand equation,
Qd = 28 - 4P
[tex]Qd\ =\ 28\ -\ 4 \ \times\ 4[/tex]
Qd = 28 - 16
Q = 12
So, the equilibrium price is 4 and equilibrium quantity is 12.
Now, we can find the Y excerpt of the demand curve by assuming Q as 0
Qd = 28 - 4P
0 = 28 - 4P
P = 7
Similarly, we can find the Y excerpt of the supply curve
Qs = -12 + 6P
0 = -12 + 6P
P = 2
The producer surplus is the difference between the market price and the supply curve
The producer surplus
= [tex]\frac{1}{2}\ \times\ base\ \times\ height[/tex]
= [tex]\frac{1}{2}\ \times\ 12\ \times\ (4-2)[/tex]
= 12
The consumer surplus
= [tex]\frac{1}{2}\ \times\ base\ \times\ height[/tex]
= [tex]\frac{1}{2}\ \times\ 12\ \times\ (7-4)[/tex]
= 18
The total economic surplus
= Consumer surplus + Producer surplus
= 18 + 12
= 30
So, the producer surplus is 12, the consumer surplus is 18, and the total economic surplus is 30.
b. There are no trade barriers and the world price is $3.
Since the world price is lower than the domestic price, the country will import rice from abroad.
At price $3, the quantity demanded will be,
[tex]Qd = 24 - 4\ \times\ 3[/tex]
Qd = 24 - 12
Qd = 16
At price $3, the quantity supplied by the domestic producers is,
[tex]Qs = -12 + 6\ \times\ 3[/tex]
Qs = -12 + 18
Qs = 6
So, the quantity imported will be,
Qd - Qs = 16 - 6 = 10
The producer surplus
= [tex]\frac{1}{2}\ \times\ base\ \times\ height[/tex]
= [tex]\frac{1}{2}\ \times\ 6\ \times\ (3-2)[/tex]
= 3
The consumer surplus
= [tex]\frac{1}{2}\ \times\ base\ \times\ height[/tex]
= [tex]\frac{1}{2}\ \times\ 16\ \times\ (7-3)[/tex]
= 32
The total economic surplus is
= Consumer surplus + Producer surplus
= 32 + 3
= 35
So, the producer surplus is 3, the consumer surplus is 32, and the total economic surplus is 35.
We see that the total economic surplus is higher after the trade. This means that the country is better off with trade.
Answer: The country is better off than in part a
Explanation:
Given the equation
Qd= 28- 4P
Qs= -12 + 6P
At equilibrium Qd = Qs
28-4P=-12 +6P
Collect like terms
28 + 12 = 6P + 4P
40 = 10 P
Divide both sides by 10
40/10 10P/10
4 = P
P = 4
Substitute the value of P into equation 1 and 2 to determine the equilibrium quantity
28 - 4 (4)
28 - 16
= 12
- 12 + 6 (4)
-12 + 24
=12
Therefore equilibrium price is $4 , equilibrium quantity is 12
To calculate consumer surplus and producer surplus
At price equilibrium price of $4, the producer is willing to supply at the price of $6, we can calculate the consumer surplus by using the formula for the area of triangle( 1/2 base* height
Base = 12
Height = 6
1/2*(12)*(6-4)
= 6*2
= 12
Since commodity price is $4 ,. Therefore any amount above the Market price of $ 4 represents the consumer surplus.
The producer surplus is the gain derived from the consumer by the producer.
Since the producer supply at price $6,
To calculate producer surplus since equilibrium price is $4, and quantity is 12
We can use the formula for area of a triangle to calculate producer surplus
1/2 base* height
Base = 12
Height=6
1/2*(12)*(6-4)
= 6*2
= 12
(B ) Suppose that there is no trade barrier and the price is $3 find Qd, As and level of import Qd-As
To calculate Qd, we use equation 1
28 - 4 ( 3)
= 28- 12
= 16
To calculate Qs, we use equation 2
-12 +6 (3)
-12 + 18
= 6
To calculate the level of import Qd - Qs
16 - 6
= 10
At price equilibrium price of $4, the producer is willing to supply at the price of $6, we can calculate the consumer surplus by using the formula for the area of triangle( 1/2 base* height
Base = 12
Height = 6
1/2*(12)*(6-4)
= 6*2
= 12
Since commodity price is $4 ,. Therefore any amount above the Market price of $ 4 represents the consumer surplus.
The producer surplus is the gain derived from the consumer by the producer.
Since the producer supply at price $6,
To calculate producer surplus since equilibrium price is $4, and quantity is 12
We can use the formula for area of a triangle to calculate producer surplus
1/2 base* height
Base = 12
Height=6
1/2*(12)*(6-4)
= 6*2
= 12
(B ) Suppose that there is no trade barrier and the price is $3 find Qd, As and level of import Qd-As
To calculate Qd, we use equation 1
28 - 4 ( 3)
= 28- 12
= 16
To calculate Qs, we use equation 2
-12 +6 (3)
-12 + 18
= 6
To calculate the level of import Qd - Qs
16 - 6
= 10
To calculate consumer surplus
1/2 base*height
1/2*16( 4-3)
8*9
8
=8
To calculate producer surplus
1/2 base* height
1/2 6( 4-3)
3*1
3
