Question

if the supply and demand functions for a commodity are given by p-q=10 and q(2p-10)=2100, what is the equilibrium price and what is the corresponding number of units supplies and demanded

Answer 1

Answer:

If p - q = 10, then p = 10 + q.  Replace the other p with this:

q(2(10 + q) - 10) = 3600

q(20 + 2q - 10) = 3600

q(10 + 2q) = 360

Answer 2

The equilibrium point of a demand and supply function is the point where both functions are equal.

The equilibrium price is 40, and the corresponding demand is 30 supplies

Given

$p- q = 10$ --- the supply function

$q(2p - 10) = 2100$ --- the demand function

Make q the subject in $p- q = 10$

$q = p - 10$

Substitute $q = p - 10$ in $q(2p - 10) = 2100$

$(p - 10)(2p - 10) = 2100$

Factor out 2

$2(p - 10)(p - 5) = 2100$

Divide both sides by 2

$(p - 10)(p - 5) = 1050$

Open brackets

$p^2 -10p - 5p + 50 = 1050$

$p^2 -10p - 5p + 50 - 1050 =0$

$p^2 -15p - 1000 =0$

Expand

$p^2 -40p + 25p- 1000 =0$

Factorize

$p(p -40) + 25(p- 40) =0$

Factor out p - 40

$(p+ 25) (p- 40) =0$

Solve for p

$p = -25$ or $p = 40$

The price cannot be negative.

So: $p =40$

Recall that:

$q = p - 10$

$q = 40 - 10$

$q = 30$

Hence, the equilibrium price is 40, and the corresponding number of supplies is 30

See attachment for the graphs of both functions

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