Demand and supply curves of a commodity are given to be D=35-3p and S=...
Solution:
Introduction:
In this question, we are given demand and supply curves of a commodity. We need to find out the amount of tax or subsidy which would have to be imposed to double the equilibrium price.
Equilibrium Price:
Equilibrium price is the price at which quantity demanded equals quantity supplied. It is the price at which there is no excess demand or excess supply in the market.
Equilibrium Quantity:
Equilibrium quantity is the quantity bought and sold at the equilibrium price.
Demand Curve:
The demand curve shows the relationship between the price of a commodity and the quantity demanded of that commodity. In this question, the demand curve is given as D=35-3p.
Supply Curve:
The supply curve shows the relationship between the price of a commodity and the quantity supplied of that commodity. In this question, the supply curve is given as S=2p.
Equilibrium Price and Quantity:
To find the equilibrium price and quantity, we need to equate the demand and supply curves.
35-3p = 2p
35 = 5p
p = 7
Substituting p=7 in the demand curve, we get:
D = 35 - 3(7) = 14
Therefore, the equilibrium price is 7 and the equilibrium quantity is 14.
Imposing Tax or Subsidy:
To double the equilibrium price, we need to increase the equilibrium price from 7 to 14. This can be done by imposing a tax or subsidy on the commodity.
- Tax: To increase the price from 7 to 14, we need to impose a tax of:
Tax = (New Price - Old Price)/Old Price
= (14-7)/7
= 1
Therefore, a tax of 100% or doubling the price would be required to achieve the desired increase in the equilibrium price.
- Subsidy: To increase the price from 7 to 14, we can also provide a subsidy on the commodity. The subsidy required to achieve the desired increase in the equilibrium price can be calculated using the formula:
Subsidy = (New Price - Old Price)/Supply Curve
= (14-7)/2(7)
= 0.5
Therefore, a subsidy of 50% would be required to achieve the desired increase in the equilibrium price.
Conclusion:
In conclusion, to double the equilibrium price of a commodity with demand curve D=35-3p and supply curve S=2p, we need to impose a tax of 100% or provide a subsidy of 50%.