SOLUTION: The supply and demand for a product are given by 2p − q = 60 and pq = 100 + 25q, respectively. Find the market equilibrium point. p,q=

Question 1167294: The supply and demand for a product are given by
2p − q = 60 and pq = 100 + 25q,
respectively. Find the market equilibrium point.
p,q=
Answer by Resolver123(6) (Show Source): You can put this solution on YOUR website!
We are given the supply and demand equations:

Supply equation: 2p - q = 60 ...................(1)
Demand equation: pq = 100 + 25q ................(2)

The market equilibrium point occurs where supply = demand, which means we need to find the values of p and q that satisfy both equations simultaneously.

Solve equation (1) for p:
From the supply equation:
2p - q = 60 => 2p = 60 + q => ........(3)

Substitute (3) into (2):
, or

Rearrange the terms into a quadratic equation
, or .

The left side of the quadratic equation can be factored as , giving q = -20 or q = 10.
Eliminate q = -20 since it is negative. Therefore, q = 10. So the equilibrium quantity is q = 10.

Substitute q = 10 into equation (3) to find the corresponding price:
. Hence, the equilibrium price is p = 35.

Thus, the market equilibrium point is (q, p) = (10, 35), which means that the market is in equilibrium when 10 units are sold at a price of $35.

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