Find the equilibrium price and quantity from the given demand and supply functions. Q d = 400 4p and Q s = 6p 10

To find the equilibrium price and quantity, we set the demand function equal to the supply function and solve for $p$. The equilibrium occurs where $Q_d=Q_s$.

Given: $$Q_d=400-4p\text{(Demand function)}$$ $$Q_s=6p-10\text{(Supply function)}$$

Step 1: Set $Q_d=Q_s$

$$400-4p=6p-10$$

Step 2: Solve for $p$

Bring all terms involving $p$ to one side and constants to the other: $$400+10=6p+4p$$ $$410=10p$$ $$p=\frac{410}{10}=41$$

So, the equilibrium price is ₹41.

Step 3: Find the equilibrium quantity ($Q$)

Substitute $p=41$ into either the demand or supply function. Using the demand function: $$Q_d=400-4(41)$$ $$Q_d=400-164=236$$

Alternatively, using the supply function: $$Q_s=6(41)-10=246-10=236$$

Thus, the equilibrium quantity is 236 units.

Verification

At $p=41$, both demand and supply match: $$Q_d=236\text{and}{Q}_s=236$$

This confirms the equilibrium point is correct.