Question

At a price of $140 there is demand for 1080 items and a supply of 420 items. At a price of $260 there is demand for 120 items and a supply of 780 items. Assuming supply and demand are linear, find the equilibrium price and quantity.

Equilibrium quantity: _____________ items
Equilibrium price: $ __________________

Answer 1

Using the concept of supply and demand, we can find the equilibrium price and quantity. With the given information, we can set up and solve equations to find the values of a, b, c, and d. By setting the demand equal to the supply, we can find the equilibrium price and quantity.

Step-by-step explanation:

From the given information, we can use the concept of supply and demand to find the equilibrium price and quantity. Let's define the demand and supply equations:

Demand: Qd = a - bP
Supply: Qs = c + dP

We can find the values of a, b, c, and d using the given information:

At $140, Qd = 1080 and Qs = 420

At $260, Qd = 120 and Qs = 780

Solving these equations, we get a = 1800, b = 2, c = 180, and d = 2.

To find the equilibrium price and quantity, we set Qd equal to Qs:

a - bP = c + dP

Substituting the values we found, we get:

1800 - 2P = 180 + 2P

4P = 1620
P = 405

Substituting this back into the demand or supply equation, we can find the equilibrium quantity:

Qs = 180 + 2(405) = 990