6 Consider the following demand and supply curves Op 5408P

6. Consider the following demand and supply curves: Op = 540-8P Qs=120+6P where QD= Quantity demanded, Qs = Quantity supplied and P-price a. Find the equilibrium price and quantity. b. If the price is pegged at $40, what problem does the producer face? How much is the disparity between Qs and Qp?

Solution

A) Equilibrium price and quantity are determined by equating demand and supply

540 - 8P = 120 + 6P

420 = 14P

P* = 30 and Q* = 540 - 8*30 = 300 units.

Hence equilibrium price is $30 per unit and equlibrium quantity is 300 units.

b) When the price is fixed at $40, the quantity demanded is 540 - 8*40 = 220 and quantity supplied is 120 + 6*40 = 360 units. This implies that there is a surplus of 360 - 220 = 140 units which is unsold. This unsold inventory of 140 units is the problem for the producer as his goods are not being sold.