Suppose the demand and supply curve of commodity X in a perfectly competitive market are given by:

q^D = 700 − p

q^S = 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?

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Solution

It is given that;

q_d = 700 − p

q_s = 500 + 3p for p > Rs 15

= 0 for 0 ≤ p < 15

The market supply is zero for any price from Rs 0 to Rs 15, this is because, for price between 0 to 15, no individual firm will produce any positive level of output (as the price is less than the minimum of AVC). Consequently, the market supply curve will be zero.

At equilibrium q_d = q_s

700 − p = 500 + 3p

− p −3p = 500 − 700

− 4p = − 200

p = 50

Equilibrium price is Rs 50.

Quantity = q_s= 500 + 3p

= 500 + 3 (50)

= 500 + 150

= 650

Therefore, the equilibrium quantity is 650 units.

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