Supply and demand in math
form
Say in general demand is expressed as
Qd = A – BP, where A and B are positive numbers.
Supply would be expressed as
Qs = C + DP where D is positive or zero and C could be any number.
To find equilibrium in the market
1) Set Qd = QS to have A – BP = C + DP
2) Collect P terms on the right and non P terms of the left to have
A – C = BP + DP
3) Rearrange to (B + D)P = A – C
4) Solve for P = (A – C)/(B + D)
5) Put this P into demand to get Q = A – B[(A – C)/(B + D)] or
Q = A[(B + D)/(B + D)] - B[(A – C)/(B + D)]
= [AD + BC]/(B + D)
Looks like a big deal but not really – let’s put in numbers.
Say demand is Qd = 18 – 2P and supply is Qs = -6 + 6P
Then to get equilibrium set Qd = Qs,
18 – 2P = -6 + 6P, or
24 = 8P, or
P = 24/8 = 3,
Put P = 3 into demand to get
Q = 18 – 6 = 12. (You could also put P = 3 into supply to see Q =
12).
So the equilibrium P = 3 and equilibrium Q = 12.
Note in our supply and demand graph we put P on the vertical
axis, so we may want to put the equations as
Demand P = (18/2) – (1/2)Qd
Supply P = (6/6) + (1/6)Qs
P
9
S
3
D
1
12
Note in our example if we had a price ceiling of 2 the Qd = 14
and Qs = 6 and so we would have a shortage of 8 units.
A price ceiling of 4 would be mean Qd = 10 and Qs = 18. This
would mean a surplus of 8 units and a surplus leads to a lower
price. Price could fall with a ceiling it just can not go above. A
price ceiling of 4 would not change the market equilibrium.
If supply is vertical you can follow all the same basic procedures
here.