Question

In a competitive market, the demand is, QD =356.3−2.6P. The supply of beef is, Qₛ =−166.4+3.4P if P≥166.4/3.4. What is the equilibrium price?

In a competitive market, the demand is, QD =356.3−2.6P. The supply of beef is, Qₛ =−166.4+3.4P if P≥166.4/3.4. What is the equilibrium quantity sold?

In a competitive market, the demand is, QD =356.3−2.6P. The supply of beef is, Qₛ =−166.4+3.4P if P≥166.4/3.4. What is the equilibrium quantity sold? What is the shortage if the price ceiling is $80 ? (Put " 0 " if there is no shortage)

Answer 1

The equilibrium price is $104.54, and the equilibrium quantity sold is 84.496 units. With a price ceiling at $80, there is a shortage of 42.7 units.The equilibrium price in the competitive market is $104.54, found by setting demand equal to supply. With a price ceiling at $80, a shortage of 42.7 units arises.

Step-by-step explanation:

To find the equilibrium price in a competitive market, we set the demand equation equal to the supply equation:

QD = Qs

356.3 - 2.6P = -166.4 + 3.4P

Add 2.6P to both sides and add 166.4 to both sides to get:

5P = 522.7

Now, divide both sides by 5:

P = 104.54

The equilibrium quantity sold can be determined by substituting the equilibrium price back into either the demand or supply equation:

QD = 356.3 − 2.6(104.54) = 356.3 − 271.804 = 84.496

If there is a price ceiling at $80, which is lower than the equilibrium price, we find the quantity demanded and the quantity supplied at this price:

QD at $80 = 356.3 - 2.6(80) = 356.3 - 208 = 148.

Qs at $80 = -166.4 + 3.4(80) = -166.4 + 272 = 105.6

The shortage is the difference between quantity demanded and quantity supplied at the price ceiling:

Shortage = QD - Qs = 148.3 - 105.6 = 42.7