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

A market is described by the following supply and demand curves: $$Q^S = 2P$$ $$Q^D = 300 - P$$ a. Solve for the equilibrium price and quantity. b. If the government imposes a price ceiling of \$90, 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, 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. 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:
$$Q^S = 2P$$ $$Q^D = 300 - P$$
a. Solve for the equilibrium price and quantity.
b. If the government imposes a price ceiling of \$90, 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, 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. 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

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 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.

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.

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.

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.

Transcript

00:01 Okay, in this question we're giving a market described by the following supply and demand functions, where the quantity supplied equals two times the price, and the quantity demanded equals 300 minus the price.

00:13 The first thing that we want to figure out is the equilibrium price and quantity.

00:18 Well, we know that the equilibrium price is such that quantity supplied should equal quantity demanded at that price.

00:27 So, in order to find this price, all we need to do is set quantized applied equal to the qualifying demanded, and we have those two functions here.

00:37 So we'll say 2p equals 300 minus p, and then just adding p to both sides, we'll have 3p equals 300, and we'll find that the equilibrium price is 100.

00:54 From this, we can also plug in the equilibrium price to either the quantity supplied or demanded to arrive at the equilibrium quantity.

01:05 And i'm going to plug it into the demand function this time.

01:09 So i will do 300 minus the equilibrium price of 100, and we will arrive at an equilibrium quantity of 200.

01:17 And of course, you could also multiply 2 by 100 and arrive at the same equilibrium quantity.

01:22 So that's part a.

01:24 For part b, we're going to impose a price ceiling, which i call pmax, of 90.

01:34 Now, recall that the equilibrium price currently is 100.

01:41 We're going to impose a maximum price below equilibrium price, such that you can't engage in market activity above a price of 90.

01:50 And so we can tell by visual inspection alone that this is going to influence equilibrium behavior.

01:56 In particular, we should end up with quantity supplied less than quantity demanded.

02:02 So i'm going to plug in this price 90 to the quantity supplied.

02:10 We'll just have 2 times 90 equals 180.

02:14 And then i will also plug in this price of 90 to the demand function.

02:19 And we'll have 300 minus 90 renders the quantity demanded to be 210.

02:26 So we see the exact behavior that we expect to see.

02:30 And in particular, we know that when quantity supplied is less than quantity demanded, there are more people interested in purchasing the good than that good is available.

02:41 In this case, we have what's known as a shortage...

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