How do you calculate equilibrium price using Qs, Qd, and price? 3 #'s given to me.

Question

Qs = 500,000, price is $20,  Qd = 700000

Answer 1

The functions linking price, demand and supply have not been given, and these are essential for finding the equilibrium price and quantity.

What we would expect is demand quantity Q_d=A-Bp where A and B are fixed numbers (unknown because not given), and, similarly, supply quantity Q_s=C+Dp. Sometimes these are written, solving for p:

p=(A-Q_d)/B and p=(Q_s-C)/D. But we have only been given one price. We therefore have to assume that p=20 when Q_s=500000 and also when Q_d=700000, so 20=(Q_s-C)/D=(500000-C)/D. Let's also assume that C=0, then 500000/D=20 and D=25000. This gives us the function Q_s=25000p.

At equilibrium, Q_s=Q_d, so 25000p=A-Bp, p(25000+B)=A, so p_e (equilibrium price)=A/(25000+B).

The equilibrium quantity Q_e=25000A/(25000+B) [using the function Q_s=25000p].

We also have Q_d=A-Bp, 700000=A-20B, so B=(A-700000)/20.

p_e=A/(25000+B)=A/(25000+(A-700000)/20)=20A/(A-200000). Clearly A>200000.

Q_e=25000p_e=500000A/(A-200000).

For example, if A=300000, then p_e=6000000/100000=$60, Q_e=Q_s=150000000000/100000=1500000.

If A=700000, p_e=14000000/500000=$28, Q_e=Q_s=700000.