Question

Qualcomm is interested in obtaining quick estimates of the supply and demand curves for rare earth metals. The firm's research department informs that the data can currently be estimated as follows Q d =2231−25PQ s =−844+50P The current equilibrium price is $41 for 1206 equivalent units available. Determine the impact of a 10% increase in demand on the existing equilibrium price and quantity?

Answer 1

A 10% increase in demand reduces the equilibrium price from $41 to approximately $38.47.

Step-by-step explanation:

To determine the impact of a 10% increase in demand on the existing equilibrium price and quantity, we need to find the new equilibrium point. First, we can calculate the current equilibrium quantity demanded (Qd) and quantity supplied (Qs) using the given equations Qd = 2231 - 25P and Qs = -844 + 50P.

At the current equilibrium price of $41, we substitute P = 41 into the equations to find Qd = 2231 - 25(41) = 1206 and Qs = -844 + 50(41) = 1206. Now, let's increase the demand by 10%.

To find the new equilibrium price and quantity, we multiply the original equilibrium quantity by 1.1 (10% increase) and substitute it into the demand equation Qd = 2231 - 25P.

We have Qd' = 1.1 * 1206 = 1326.6. Solving the equation 1326.6 = 2231 - 25P for P, we find P ≈ $38.47, which is the new equilibrium price.

Therefore, the impact of a 10% increase in demand is a reduction in the equilibrium price from $41 to approximately $38.47.