Q.Consider a market consisting of identical farms producing the same quality of wheat. Suppose the market demand curve and the market supply curve for wheat are given by $q_D = 200 - p$ for $0 \le p \le 200$ and $q_D = 0$ for $p > 200$; $q_S = 120 + p$ for $p \ge 10$ and $q_S = 0$ for $0 \le p < 10$, where $q_D$ and $q_S$ denote the demand for and supply of wheat (in kg) respectively and $p$ denotes the price of wheat per kg in rupees. Find the equilibrium price and quantity, and examine the situation at prices below and above the equilibrium price.

The equilibrium condition is market demand equals market supply: $q_D = q_S$.

Set the two equations equal:

Solve for $p$:

Substitute $p = 40$ into either equation to find equilibrium quantity. Using demand:

Using supply gives the same: $q_S = 120 + 40 = 160$.

Thus equilibrium price is ₹40 per kg and equilibrium quantity is 160 kg.

Now examine situations away from equilibrium.

Price below equilibrium (say $p < 40$): At any such price, $q_D > q_S$. For example, at $p = 20$, $q_D = 180$ and $q_S = 140$, giving excess demand of 40 kg. This shortage pushes the price upward toward equilibrium.

Price above equilibrium (say $p > 40$): Here $q_S > q_D$. For example, at $p = 60$, $q_D = 140$ and $q_S = 180$, giving excess supply of 40 kg. This surplus pushes the price downward toward equilibrium.

The market clears only at $p = 40$, where there is neither excess demand nor excess supply.

The Core Idea: Market Demand Aggregation

A market reaches equilibrium when the plans of buyers and sellers are mutually consistent — that is, when the quantity consumers want to buy exactly matches the quantity producers want to sell. This is not a coincidence; it is the natural outcome of price adjustment. If price is too high, unsold stock piles up and sellers cut price; if price is too low, queues form and buyers bid price up. Only at the equilibrium price do both sides feel satisfied.

Here, we have a perfectly competitive market for wheat. All farms are identical and produce homogeneous wheat, so no single buyer or seller can influence price. The market demand curve $q_D = 200 - p$ tells us that as price rises, quantity demanded falls — a standard downward-sloping demand curve. The market supply curve $q_S = 120 + p$ (for $p \ge 10$) tells us that as price rises, quantity supplied rises — an upward-sloping supply curve.

Step-by-Step Working

Step 1: Set quantity demanded equal to quantity supplied.

Since both $q_D$ and $q_S$ are expressed in terms of $p$, we write:

Step 2: Solve for $p$.

Bring terms involving $p$ to one side:

So the equilibrium price is ₹40 per kg.

Step 3: Find equilibrium quantity.

Substitute $p = 40$ into either the demand or supply equation. Using demand:

Using supply:

Both give the same result. Equilibrium quantity is 160 kg.

What Happens Away from Equilibrium?

At a price below equilibrium, say ₹30:

Demand: $q_D = 200 - 30 = 170$ kg

Supply: $q_S = 120 + 30 = 150$ kg

Excess demand = $170 - 150 = 20$ kg. Buyers want more wheat than sellers are willing to supply. This shortage puts upward pressure on price — buyers compete, and price rises toward ₹40.

At a price above equilibrium, say ₹50:

Demand: $q_D = 200 - 50 = 150$ kg

Supply: $q_S = 120 + 50 = 170$ kg

Excess supply = $170 - 150 = 20$ kg. Sellers cannot sell all their wheat. This surplus forces price downward as sellers undercut each other, again moving toward ₹40.

Conclusion

The market clears at ₹40 per kg with 160 kg of wheat traded. Any deviation from this price creates either excess demand (shortage) or excess supply (surplus), and the price mechanism automatically pushes the market back to equilibrium. This is the invisible hand at work in a competitive market.