A market is described by the following supply and demand...

A market is described by the following supply and demand curves: $$ \begin{array}{l} Q^{S}=2 P \\ Q^{D}=300-P \end{array} $$ a. Solve for the equilibrium price and quantity. b. If the government imposes a price ceiling of 90 dollar, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus? c. If the government imposes a price floor of 90 dollar, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus? d. Instead of a price control, the government levies a tax on producers of 30 dollar. As a result, the new supply curve is: $$ Q^{S}=2(P-30) $$ Does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?

A market is described by the following supply and demand curves:
$$
\begin{array}{l}
Q^{S}=2 P \\
Q^{D}=300-P
\end{array}
$$
a. Solve for the equilibrium price and quantity.
b. If the government imposes a price ceiling of 90 dollar, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?
c. If the government imposes a price floor of 90 dollar, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?
d. Instead of a price control, the government levies a tax on producers of 30 dollar. As a result, the new supply curve is:
$$
Q^{S}=2(P-30)
$$
Does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?

Key Concepts

Shortage and Surplus

Shortage and surplus are terms used to describe disequilibrium in a market. A shortage occurs when the quantity demanded exceeds the quantity supplied at a given price, often as a result of binding price ceilings. Conversely, a surplus happens when the quantity supplied exceeds the quantity demanded, which is typically induced by binding price floors. These conditions signal market inefficiencies and potential corrective actions.

Tax Incidence

Tax incidence describes the manner in which the burden of a tax is distributed between buyers and sellers. When a tax is levied on producers, it effectively shifts the supply curve upward by the amount of the tax. This adjustment results in a new equilibrium where the price paid by consumers is higher and the price received by producers is lower, even though the total market quantity may change.

Price Ceiling

A price ceiling is a government-imposed limit on how high a price can be charged for a product. When set below the equilibrium price, it becomes binding and typically leads to a shortage because the quantity demanded exceeds the quantity supplied at the legally allowed price.

Market Equilibrium

Market equilibrium is the point at which the quantity supplied equals the quantity demanded. This condition is achieved by equating the supply and demand equations and solving for the price and quantity that balance both sides of the market. At this point, there is no inherent tendency for the price or quantity to change, as the market forces are in balance.

Price Floor

A price floor is a government-imposed minimum price that can be charged for a product. When the floor is set above the equilibrium price, it is binding and generally results in a surplus, as the quantity supplied exceeds the quantity demanded at that minimum price. However, if the price floor is below the natural equilibrium, it is non-binding and the market remains in equilibrium.

Transcript

00:01 All right, here we're given a couple of supply and demand curves for any market.

00:05 We have a quantity supplied equal to 2p and a quantity demanded equal to 300 minus p.

00:11 We first want to find what this equilibrium is.

00:14 So we know that our equilibrium is going to be the point at which these two points cross.

00:18 And we want to know what our quantity is down here and what our price is at this equilibrium.

00:24 So to do that, we can just set these two curves equal to one another.

00:28 So we can do 2p, set 2p equal to 300 minus p.

00:35 And let's go ahead and solve for p here.

00:38 Adding p to both sides with 3p is equal to 300.

00:41 And dividing both sides by 3 gives us a price, which is equal to 100.

00:46 So there's one piece of our equilibrium.

00:48 Now to find the quantity, we can just plug this back into either our supply or demand curve because we know that that quantity is the same for both.

00:56 So let's plug it into our quantity supplied.

00:58 Which is equal to 2p, so multiplying 2 times 100.

01:03 That gives us a quantity which is equal to 200.

01:06 All right, so these points down here, you can see that we have a quantity of 200 and a price of 100.

01:19 Now let's suppose that the government imposes a price ceiling of $90.

01:24 So that's going to sit somewhere.

01:26 We can see that our equilibrium was 100, so it's now going to sit somewhere beneath that.

01:30 So suppose $90 is right here at a price.

01:35 Price of 90, we want to know whether or not there is a shortage or a surplus that's occurring here or neither if that's the case.

01:43 What we can see here is that our new quantity supplied sits here and our new quantity demanded is going to sit over here.

01:52 That's at that price.

01:54 So it seems pretty obvious right here that when our supply and our quantity demanded over here that we have some gap that exists.

02:04 So that's going to be the shortage that we're running into.

02:07 But let's determine how much that shortage actually is.

02:11 So all we need to do is plug our price of 90 into our quantity demanded and our quantity supplied functions.

02:19 So doing that, we have our quantity supplied with the price of 90 is 2 times 90.

02:26 It tells us that our quantity supplied is 180.

02:30 To the same for our quantity demanded, which is 300 minus 90.

02:38 That gives us a quantity demanded, which is equal to 210.

02:42 210, sorry, if i can do basic math.

02:45 So what we can see here now is that there's a $30 unit difference here...

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