Find equilibrium price and quantity where P = 6+Q²/4 and Q =⌡36-P

Question

equilibrium price and quantity

Answer 1

Rewrite:

P=6+Q²/4, P=J36-Q. Equilibrium on price (and therefore quantity Q) occurs when these two expressions for price are equal:

6+Q²/4=J36-Q, 24+Q²=4J36-4Q,

Q²+4Q=4J36-24,

Q²+4Q+4=4J36-20,

(Q+2)²=4J36-20,

Q+2=√(4J36-20), Q=2√(J36-5)-2 (because Q cannot be negative and must be an integer).

We don't know the numerical value of J36, but clearly J36≥5. Also, since Q>0, √(J36-5)>2, so J36-5>4, J36>9.

For example, if J36=21, Q=6 and P=15; if J36=69, Q=14, P=55; if J36=1029, Q=62, P=967. If $30<J36≤$41, 8<Q≤10, $22<P≤$31.

(NOTE: The character ⌡resembling a capital letter "J" may have been intended to represent something else which cannot be determined. The character appears to be the lower half of an integral sign ∫.)