Question

The demand and supply functions for oil in a small isolated country are Qd = 210 − 1.5P and Qs = −140+ 2P , where P is the price per barrel and quantities are in millions of barrels per year. a. Find the free market equilibrium for the economy.

b. The Government imposes a price floor at $110 per barrel.

If this price floor is implemented and the government is forced to buy the excess,

i. What is the amount of Government spending?

ii. What is the new level of producer surplus? Draw a graph to support your answer.

c. If the Government withdraws the ‘surplus purchase assurance’, what is the producer surplus now?

d. Without Government ‘surplus purchase assurance’, should the price floor be implemented?

Answer 1

Sol :

a) Market equilibrium is at the point where Demand is eqaul to the supply .

i.e Qd = Qs

Qd = 210 - 1.5P

Qs = -140 + 2P

210 - 1.5P = -140 + 2P

210 + 140 = 3.5P

350 = 3.5P

350/3.5 P

100 = P ( equilibrium Price)

Q = 210 - 1.5 x 100 = 60 ( equilibrium Quantity)

b) if the government imposes the price floor of $110 per barrel. whereas market equilibrium price is $100 .

Qs (at $110 price) = -140 + 2P

                               = -140 + 2(110) = 220 - 140

                              = 80

Qd = 210 - 1.5P

      = 210 - (1.5 x 110)

      = 210 - 165

      = 45

i) excess supply is equal to = Qs - Qd

                                            = 80 - 45 = 35

So, Amount of government spending is equal to = Price at floor price x excess quantity

                                                                             = $110 x 35 = $3850

ii) Producer surplus is the area beow the price level and above the supply curve .

so , new producer surplus after price floor and when government provides the assurance about the excess supply is

when price = $110 and quantity supplied is 80 units

so , area of producer surplus = 1/2 x base x height

                                              = 1/2 x 110 ( Price) x 80(quantity)

                                               = 4400

c) when the government withdraws the ' surplus purchase assurance' then , the producer surplus reduces, where price = $110 and quantity sold is equal to 45

.this producer surplus is equal to the outlined shaped in the given diagram .

d) No, without the surplus purchase assurance government should not implement the price floor because there will be excess supply in the market , if price floor is implemented and both the producer and consumer will be worse off than before.

Area fo producer surplus = 1/2 x (