Suppose the demand and supply curve of commodity X in a perfectly competitive market are given by: = 700 - p; = 500 + 3p for p 15; = 0 for 0 p < 15. 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?
Reason for Zero Supply: The market supply of commodity X is zero at any price less than Rs 15 because the market consists of identical firms with the same cost structure. At prices below Rs 15, firms cannot cover their costs of production. Since the price is insufficient to recover costs, no firm is willing to supply the commodity, resulting in zero market supply.
Equilibrium Price: At equilibrium, market demand equals market supply.
=
700 - p = 500 + 3p
700 - 500 = 3p + p
200 = 4p
p = Rs 50*
Since p* = 50 15, this equilibrium price is valid.
Equilibrium Quantity: Substituting p* = 50 in the demand equation:
q* = 700 - 50 = 650 units
Alternatively, substituting in the supply equation:
q* = 500 + 3(50) = 500 + 150 = 650 units
Thus, at equilibrium, 650 units of commodity X will be produced.
Explanation
This question tests understanding of market equilibrium under perfect competition. The supply curve has a threshold price (Rs 15) below which supply is zero because firms cannot cover costs. The equilibrium is found by equating demand and supply functions. Since the calculated equilibrium price (Rs 50) exceeds the threshold (Rs 15), the supply function is valid at this price.
Solution Steps
Step 1: Identify that supply is zero below Rs 15 because firms cannot cover production costs at lower prices
Step 2: Set market demand equal to market supply: 700 - p = 500 + 3p
Step 3: Solve for equilibrium price: 200 = 4p, therefore p* = Rs 50
Step 4: Verify that p* 15 (valid since 50 15)
Step 5: Calculate equilibrium quantity: q* = 700 - 50 = 650 units