demand and supply equations are p²+ q²= 20 and 2p + q = 8 respectively where p is the price and q is the quantity. find equilibrium price and quantity
Answers
Answer:
(a) Market equilibrium is struck when:
Market Demand = Market supply
Or, Q
d
=Q
s
1000−p=700+2p
⇒2p+p=1000−700
⇒3p=300
⇒p=100
wHEN $$p=10, { Q }_{ d }=1000-p $$
=1000−100=900
Equilibrium price = 100.
Equilibrium quantity = 900
(b) When price of an input used to produce salt has increased, new equilibrium price and equilibrium quantity is achieved when:
1000−p=400+2p
⇒2p+p=1000−400
⇒3p=600
⇒p=200
When p=200, Q
d
=1000−p
=1000−200=800
New equilibrium price = 200.
New equilibrium quantity = 800.
Owing to increase in input price, supply curve shifts backward. Consequently, equilibrium price is expected to rise and equilibrium quantity is expected to fall., In tune with this expected result, the new equilibrium price has risen from Rs.100 to Rs.200 and equilibrium quantity has decreased from 900 to800.
(c) When GST is imposed, the supply equation changes as under:
Q
d
=700+2(p−3) [ out of the price charged producer has to pay Rs.3 to the government ]
Equating supply and demand equations, the equilibrium price is achieved, as under:
1000−p=700+2(p−3)
⇒1000−p=700+2p−6
⇒2p+p=1000−700+6
⇒3p=306
⇒p=102
Equilibrium quantity:
1000−102=898
Or
700+2(102−3)=700+198
=898
After GST,
Equilibrium price increases from Rs.100 to Rs.102.
Equilibrium quantity reduces from 900 to 898.
Answer:
(a) Market equilibrium is struck when:
Market Demand = Market supply
Or, Q
d
=Q
s
1000−p=700+2p
⇒2p+p=1000−700
⇒3p=300
⇒p=100
wHEN $$p=10, { Q }_{ d }=1000-p $$
=1000−100=900
Equilibrium price = 100.
Equilibrium quantity = 900
(b) When price of an input used to produce salt has increased, new equilibrium price and equilibrium quantity is achieved when:
1000−p=400+2p
⇒2p+p=1000−400
⇒3p=600
⇒p=200
When p=200, Q
d
=1000−p
=1000−200=800
New equilibrium price = 200.
New equilibrium quantity = 800.
Owing to increase in input price, supply curve shifts backward. Consequently, equilibrium price is expected to rise and equilibrium quantity is expected to fall., In tune with this expected result, the new equilibrium price has risen from Rs.100 to Rs.200 and equilibrium quantity has decreased from 900 to800.
(c) When GST is imposed, the supply equation changes as under:
Q
d
=700+2(p−3) [ out of the price charged producer has to pay Rs.3 to the government ]
Equating supply and demand equations, the equilibrium price is achieved, as under:
1000−p=700+2(p−3)
⇒1000−p=700+2p−6
⇒2p+p=1000−700+6
⇒3p=306
⇒p=102
Equilibrium quantity:
1000−102=898
Or
700+2(102−3)=700+198
=898
After GST,
Equilibrium price increases from Rs.100 to Rs.102.
Equilibrium quantity reduces from 900 to 898.