Q.Suppose the demand and supply curve of commodity X in a perfectly competitive market are given by: ; for and for . Assume that the market consists of identical firms. Identify the reason behind the market supply of commodity X being zero at any price less than Rs 15. What will be the equilibrium price for this commodity? At equilibrium, what quantity of X will be produced?
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Start your 14-day free trial to unlock the full solution →Below Rs 15, no firm covers its minimum average variable cost, so all shut down and market supply is zero. Equilibrium occurs where , yielding price Rs 50 and quantity 650 units.
Why supply is zero below Rs 15
A firm in a perfectly competitive market will produce only if the price covers at least its average variable cost (AVC). If price falls below minimum AVC, the firm loses less by shutting down and producing nothing—it still bears fixed costs, but avoids the additional variable costs that would exceed revenue.
Here, the supply curve is defined only for , while for . This tells us that Rs 15 is the shut-down price: the minimum AVC of each identical firm is Rs 15. Below that threshold, revenue per unit cannot cover the variable cost per unit, so every firm exits production in the short run. Because the market comprises identical firms, when all of them shut down simultaneously, aggregate market supply drops to zero.
The kink at is the market's shut-down point. It reflects the lowest price at which firms are willing to supply any positive quantity—precisely where price equals minimum AVC.
Finding equilibrium price and quantity
Equilibrium in a perfectly competitive market occurs where quantity demanded equals quantity supplied. Since supply is positive only for , we work with the supply function in that range.
Step 1. Set :
Step 2. Collect terms:
Step 3. Solve for :
Because , this price lies in the valid range where firms produce. …
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