Question

12. the market for rice in an east asian country has demand and supply given by Qd = 28 -4P and Qs = -12 + 6P, where quantities denote millions of bushels per day. a. if the domestic market is perfectly competitive, find the equilibrium price and quantity of rice. Compute the triangular areas of consumer surplus and produces surplus. b. now suppose that there are no trade barriers and the world price of rice is $ 3. Confirm that the country will import rice. Find Qd, Qs and the level of import, Qd - Qs. show that the country is better off than in part ( a ), by again computing consumer surplus and producer surplus.

Answer 1

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

Answer 2

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

$Qd\ =\ 28\ -\ 4 \ \times\ 4$

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

= $\frac{1}{2}\ \times\ base\ \times\ height$

= $\frac{1}{2}\ \times\ 12\ \times\ (4-2)$

= 12

The consumer surplus

= $\frac{1}{2}\ \times\ base\ \times\ height$

= $\frac{1}{2}\ \times\ 12\ \times\ (7-4)$

= 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,

$Qd = 24 - 4\ \times\ 3$

Qd = 24 - 12

Qd = 16

At price $3, the quantity supplied by the domestic producers is,

$Qs = -12 + 6\ \times\ 3$

Qs = -12 + 18

Qs = 6  

So, the quantity imported will be,

Qd - Qs = 16 - 6 = 10

The producer surplus

= $\frac{1}{2}\ \times\ base\ \times\ height$

= $\frac{1}{2}\ \times\ 6\ \times\ (3-2)$

= 3

The consumer surplus

= $\frac{1}{2}\ \times\ base\ \times\ height$

= $\frac{1}{2}\ \times\ 16\ \times\ (7-3)$

= 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.