Question #70983

demand and supply in the wheat market are given by:
QD=20-10P and QS= -5+10P
where Q is millions of cars and P is price per car.
a) Find the equilibrium price and quantity.
b) Calculate the price elasticity of demand at equilibrium and interpret your result.
c) Suppose that the government wishes to support farm income and thus sets a price of $1.50, Find the size of the farm surplus or shortage.
d) What is the cost of this program to the government?
e) If the government introduces a tax of $1, find the new supply curve and the equilibrium price and quantity.

Expert's answer

QD=20-10P and QS= -5+10P, where Q is millions of cars and P is price per car.

a) The equilibrium price and quantity are:

Qd = Qs,

20 - 10P = -5 + 10P,

20P = 25,

P = $1.25,

Q = 20 - 10*1.25 = 7.5 millions of cars.

b) The price elasticity of demand at equilibrium is:

Ed = -2.5/0.25*1.25/7.5 = -1.66, so demand is elastic.

c) If P = $1.50, then:

Qd = 5 millions of cars, Qs = 10 millions of cars, so there is a surplus of 5 millions of cars.

d) The cost of this program to the government is 1.5*5 = $7.5 million.

e) If the government introduces a tax of $1, then the new supply curve is: Qs = -5 + 10*(P - 1) = -15 + 10P.

The new equilibrium price and quantity are:

20 - 10P = -15 + 10P,

20P = 35,

P = $1.75,

Q = 20 - 10*1.75 = 2.5 millions of cars.

a) The equilibrium price and quantity are:

Qd = Qs,

20 - 10P = -5 + 10P,

20P = 25,

P = $1.25,

Q = 20 - 10*1.25 = 7.5 millions of cars.

b) The price elasticity of demand at equilibrium is:

Ed = -2.5/0.25*1.25/7.5 = -1.66, so demand is elastic.

c) If P = $1.50, then:

Qd = 5 millions of cars, Qs = 10 millions of cars, so there is a surplus of 5 millions of cars.

d) The cost of this program to the government is 1.5*5 = $7.5 million.

e) If the government introduces a tax of $1, then the new supply curve is: Qs = -5 + 10*(P - 1) = -15 + 10P.

The new equilibrium price and quantity are:

20 - 10P = -15 + 10P,

20P = 35,

P = $1.75,

Q = 20 - 10*1.75 = 2.5 millions of cars.

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