Question

ASAP please

200 5. Suppose you are given the following inverse demand function, p= and the inverse supply Q+1 function, p=5+0.5Q. With p on the vertical axis and Q on the horizontal, draw these two functions. Also solve for the equilibrium Q" and equilibrium price p*.

Answer 1

Demand function:

$\small P = \frac{200}{Q+1}$

Supply function:

P = 5 +0.50

Intersection of both function will be the equilibrium Q^* and equilibrium P^*.

$\small \frac{200}{Q+1}=5+0.5Q$

200 = 50 +5 +0.50 +0.50

0.502 +5.50 - 195 = 0

$\small Q^{2}+11Q-390=0$

$\small Q = \frac{-11\pm \sqrt{(11)^{2}-4\times (-390)}}{2}$

$\small Q = \frac{-11\pm \sqrt{121+1560}}{2}$

$\small Q = \frac{-11\pm \sqrt{1681}}{2}$

$\small Q = \frac{-11\pm 41}{2}$

$\small Q = -26,15$

But Q which is quantity cannot be negative.

Hence Q = 15

P = 5 + 0.5x15 = $12.5

P = 12.5

Therefore,

Equilibrium Q^* is 15 and equilibrium P^* is 12.5.