Q.Suppose the demand and supply curves of salt are given by: $q_D = 1{,}000 - p$; $q_S = 700 + 2p$.

Market equilibrium is established when the quantity demanded by consumers equals the quantity supplied by producers.

(a) To find the equilibrium price and quantity, we set the demand and supply equations equal to each other:

$q_D = q_S$

$1{,}000 - p = 700 + 2p$

$1{,}000 - 700 = 2p + p$

$300 = 3p$

$p = \frac{300}{3}$

$p = 100$

Now, substitute the equilibrium price back into either the demand or supply equation to find the equilibrium quantity:

$q_D = 1{,}000 - 100 = 900$ …

In economics, the concept of market equilibrium is fundamental. It represents a state where the forces of demand and supply are balanced, resulting in a stable price and quantity in the market. At this point, the quantity that consumers are willing and able to buy (quantity demanded) exactly matches the quantity that producers are willing and able to sell (quantity supplied). There is no pressure for the price to change, as neither a surplus nor a shortage exists.

(a) Finding the initial equilibrium price and quantity

To find the equilibrium, we set the quantity demanded equal to the quantity supplied.

1. Set demand equal to supply: Given the demand curve $q_D = 1{,}000 - p$ and the supply curve $q_S = 700 + 2p$.

2. Solve for the equilibrium price ($p$): Rearrange the equation to isolate $p$:

The equilibrium price is Rs 100.

3. Substitute the equilibrium price back into either the demand or supply equation to find the equilibrium quantity ($q$):

Using the demand equation:

Using the supply equation (as a check):

The equilibrium quantity is 900 units.

(b) Impact of an increase in input price

When the price of an input used to produce salt increases, it raises the cost of production for firms. This means that at any given price, producers are now willing to supply less salt than before, or they require a higher price to supply the same quantity. This situation is represented by a leftward (or upward) shift of the supply curve.

Our expectation is that an increase in production costs, leading to a leftward shift in supply, will result in a higher equilibrium price and a lower equilibrium quantity. Let's verify this with the new supply curve $q_S = 400 + 2p$.

1. Set the original demand equal to the new supply: The demand curve remains $q_D = 1{,}000 - p$. The new supply curve is $q_S = 400 + 2p$.

2. Solve for the new equilibrium price ($p'$):

The new equilibrium price is Rs 200.

3. Substitute the new equilibrium price back into the demand equation to find the new equilibrium quantity ($q'$):

The new equilibrium quantity is 800 units.

The change conforms to our expectation: the equilibrium price increased from Rs 100 to Rs 200, and the equilibrium quantity decreased from 900 units to 800 units. This is a standard outcome when supply contracts due to higher production costs.

(c) Impact of a government tax

When the government imposes a tax of Rs 3 per unit of salt sold, it directly affects the supply side of the market. For every unit sold, the producer must now pay Rs 3 to the government. This means that if consumers pay a price $p$, the producer effectively receives only $p - 3$. Therefore, the supply curve shifts upwards by the amount of the tax.

To incorporate the tax into the supply equation, we replace $p$ with $(p-3)$ in the original supply function.

1. Formulate the new supply curve with the tax: The original supply curve is $q_S = 700 + 2p$. …