Economic math problem about price ceiling?

Question

I'm studying the most basic economics in college right now. This is an easy concept however I don't understand why.

Qd = 100 - 2P, where P is price and Qd is Quantity Demanded
Qs = 2P - 20, where P is price and Qs is Quantity Supplied
Suppose the gov enacts a price ceiling of 40. At the new price, is there ane excess demand, excess supply, or neither? What is the new market price and qty bought and sold?

Now, I thought it was excess demand because if you plug in the price ceiling of 40 for P in both equations, you get 20 as Q for the supply curve and 60 for the demand curve. This means there will only be 20 sold while 60 are for sale, so there's an extra 40 not being sold, therefore its an excess supply..

However the answer is there's NO excess and apparently my 20 and 60 are wrong too. The grader didn't explain why.

DO YOU KNOW WHY? =)

Answer 1

my best idea is that with the price ceiling occurring above the natural equilibrium point, the ceiling is kind of a moot point.

For instance at equilibrium Qs = Qd

100-2P = 2P - 20
120 = 4P => P = 30

That being said the market will fall into equilibrium at the price of 30 since the price ceiling really has no effect due to it being at 40 which is above the equilibrium price of 30.

Since the market is in equilibrium, there is no excess supply or demand.

The equilibrium price is now 30, and putting 30 into either equation nets a quantity of 40.

This is how I understand it should work, I hope this helps.

Answer 2

If the ceiling is 40 then I see nothing wrong with your solutions at all. There's only two possibilities I see (unless I'm totally missing something):

1 - the solution is wrong and your answer is in fact correct.
2 - the price ceiling is actually 30, because with the given equations a price ceiling of 30 is the only one that would result in equilibrium (and no excess).

Answer 3

prevalent interest: revenues cost = $10 ingredients = $6 income/sale(cost - ingredients) = $4 revenues 20 necklaces x P/s 4 = income 80 a million dollar strengthen = revenues 18 necklaces x P/s 5 = income ninety 2 dollar strengthen = revenues sixteen necklaces x P/s 6 = income ninety six 3 dollar strengthen = revenues 14 necklaces x P/s 7 = income ninety 8 4 dollar strengthen = revenues 12 necklaces x P/s 8 = income ninety six that's in straightforward terms a layman's form of calculation. I ignore a thank you to get this one on a formula taught in our classification and my classmate borrowed my e book so that's it for now.