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Suppose there is a market consisting of identical firms producing the same quality of salt.

Suppose the market demand curve and the market supply curve for salt are given by:

QD={350−pfor 0≤p≤3500for p>350Q_D = \begin{cases} 350 - p & \text{for } 0 \leq p \leq 350 \\ 0 & \text{for } p > 350 \end{cases}

QS={220+pfor p≥100for 0≤p<10Q_S = \begin{cases} 220 + p & \text{for } p \geq 10 \\ 0 & \text{for } 0 \leq p < 10 \end{cases}

Where QDQ_D and QSQ_S denote the demand for and supply of salt (in kg) respectively and pp denotes the price of salt per kg in rupees.

Which of the following expressions will be used for calculating excess supply of salt in the market?

Solution

✅ Correct Option: 3

The market demand and supply equations are given as:

QD=350−pQ_D = 350 - p

QS=220+pQ_S = 220 + p


Excess supply is defined as the difference between the quantity supplied and the quantity demanded at a given price pp:

Excess Supply=QS−QD\text{Excess Supply} = Q_S - Q_D

Substituting the given expressions:

Excess Supply=(220+p)−(350−p)\text{Excess Supply} = (220 + p) - (350 - p)

=220+p−350+p= 220 + p - 350 + p

=2p−130= 2p - 130

=2(p−65)= 2(p - 65)


Based on the provided equations, the expression for excess supply is 2(p−65)2(p - 65).

However, the NTA answer key specifies the answer as 2(p−35)2(p - 35).

This result 2(p−35)2(p - 35) corresponds to a scenario where the equilibrium price is 3535, whereas the given equations QD=350−pQ_D = 350 - p and QS=220+pQ_S = 220 + p result in an equilibrium price of 6565.

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