DEMAND AND SUPPLY

QUESTION

Imagine a small island with a competitive fast food industry producing pies and sandwiches which are viewed by consumers as substitutes.

Let the demand for pies be:

(1)

Where D1 is daily demand for pies, P1 is price of pies, P2 is price of sandwiches and Y is income.

Assume the supply of pies can be described by:

(2)

Where S1 is supply of pies and the market clears so:

(3)

Assume income, Y, is $2000 and the price of sandwiches is P2 = $3. Further, assume the market always clears, there is no Teaching Period 1, 2012 5

SOLUTION

Answer 1:

Demand for pies is given by the equation

D₁= 1000-200 P₁+ 200 P₂ +Y

Supply for pies is : S₁ = 300 P₁

Market is in equilibrium. So, D₁ = S₁

P₂= $3

Y= $ 2000

1) Equilibrium price for pies is calculated by equating the demand and supply functions

D₁ = S₁

1000-200 P₁+ 200 P₂ +Y = 300 P₁

Putting the value of p₂ and Y in the above equation, we get

1000-200 P₁+ 200 (3)+ 2000 = 300 P₁ 

1000- 200 P₁ + 600 +2000= 300P₁

500 P₁ = 3600

P₁= $ 7.20

2) Number of pies produced and purchased at this price is calculated by putting this value in the supply function:

S₁= 300 P₁

= 300 X 7.20 = 2160 pies

3) Under competitive market structure, producer surplus is the area below the equilibrium price, and above the supply curve.

For calculating it, we first equate the supply curve with 0

300 X P₁ =0

P₁= 0

Producer surplus = ½ Q^e (P^e – P)

Where, Q^e is the equilibrium quantity and P^e is the equilibrium price.

= ½ X 2160 (7.20 -0)

= $ 7776

Answer 2:

When the tax of $ 2 per unit is imposed, the supply curve shifts upwards. New supply curve is given by the equation

S₁ = 300( P₁ – 2)

S₁ = 300 P₁ – 600

1) equilibrium price to the consumers is calculated by equating the  new supply function with the demand function

S₁ = D₁

300 P₁ -600 = 1000-200 P₁ + 600+ 2000

500 P₁ = 4200

P₁ = $ 8.4

2) equilibrium Price to producers is calculated by subtracting amount of tax from the price paid by consumer i.e. 8.4- 2 = $ 6.4 is the equilibrium price of the producer.

3)number of pies produced and sold at this equilibrium price is calculated by putting P₁= $ 8.4 in the new supply function

S₁ = 300 (8.4-2) = 1920 pies

4) tax revenue = 2X 1920 =$ 3840

Part 3:

S₂= 1000+ 100 P₁

Now the total supply function is the summation of S₁ and S₂

i.e. S_total = S₁ + S₂

S_total = 300 P₁ + 1000+ 100 P₁

Equating the given demand function with the above supply function, we get the new equilibrium price at which the pies will be traded

1000- 200 P₁ + 200(3) + 2000 = 300 P₁ + 1000+ 100 P₁

3600 -200 P₁ = 400 P₁ + 1000

600 P₁ = 2600

P₁= 4.33

Quantity of pies imported from the next door is calculated by putting the above value of P₁  in the supply function S₂

= 1000+ 100(4.33)

=1433 pies

JG36

But you can order it from our service and receive complete high-quality custom paper.  Our service offers Economics  essay sample that was written by professional writer. If you like one, you have an opportunity to buy a similar paper. Any of the academic papers will be written from scratch, according to all customers’ specifications, expectations and highest standards.”