if demand=500-p and supply=300+p what is equlibrium price/quantity if there is a quota restricting more than 50 units to be sold?

Question

if demand=500-p and supply=300+p what is equlibrium price/quantity if there is a quota restricting more than 50 units to be sold?

Answer 1

With the quota, do you mean "NO more than 50"?

Without the quota, the equilibrium price and quantity would be where supply=demand or (500-p)=(300+p) -- solve or p. I get p=100, ergo Qd=Qs=400.

If more than 50 must be sold, no problemo. If no more than 50, and the quota is enforced, then price will go to 450 and some lucky sellers will make a bundle.