# Numb3rs 516: Cover me

In this episode Charlie gets an idea of how to stop the spread of a new illegal drug, Hawaiian Ice. He claims that the drug is in its 'infancy' meaning that there is only a few buyers and sellers on the streets. Charlie's idea is that if the department buys most of the Hawaiian Ice, it would lead to shortage in the supply and loss of interest from the potential clients. His plan seems to be working well at first, but one of the dealers turns out to be smarter than Charlie thought. The dealer wants to corner the market, so that he can set his price on Ice. But even after the operation succeeds and all of the Ice is off the market, Charlie realizes that some other drug will take its place.

## Economic Modeling Theory

The most fundamental notion in economics is that of Supply and Demand. The idea is that a change in either one would result in corresponding change in the price for the item. Let's talk about economics of chewing gum in New York. The Supply then corresponds to the amount of chewing gum that gets produced and sold in New York. The Demand is the amount of chewing gum that all residents of New York are willing to buy at a given price.

First let's consider just the Law of Demand.

## Law of Demand

Activity 1: Think of your favorite brand of chewing gum. Below we will refer to this brand as ''Fave'' and let's assume that you usually buy three packs of gum a month. Let P dollars be the current price of ''Fave'' in the stores.
1. If a pack of gum of any brand costs exactly the same as ''Fave'', P, which brand would you buy? How many packs are you going to buy this month?
2. Now say the price of ''Fave'' went up by 30 cents, but that other chewing gum still cost P dollars. Which brand would you buy now? How many packs are you going to buy this month?
3. Now say the price of ''Fave'' is P+2, two dollars more than usual price, but that other chewing gum still cost P dollars. Which brand would you buy now? How many packs are you going to buy this month?

What you probably experienced while answering these questions is the law of demand. The law of demand captures the inverse relationship between the price and the amount of good that the consumers are willing to buy (providing all other variables, such as prices of similar goods, stay constant).

The following picture illustrates the law of demand:

The above picture shows how law of demand works - the higher the price of a item, the less people will demand that item. Notice as the price goes down from P1 to P2, the quantity that the consumer is willing to buy goes up from Q1 to Q2. Similarly, as price goes up from P3 to P2, the consumers interest in the product drops down from Q3 to Q2. This shows the inverse relationship between the price and the quantity consumers are willing to buy.

## Law of Supply and Demand

Now that we've considered the Law of Demand alone, let's look at the law of Supply and Demand. As we've mentioned this law governs the price of the good based on the goods' supply and demand amounts to maintain the equilibrium in the market.

In a small town in Midwest, the ''Bike Comp'' company is about to release a new type of bicycles. The company projected that about 20 people would like to buy this type of bicycle if it were to cost no more than \$80, thus it supplied 20 bicycles to the sporting goods store in the town. However, it turned out that their projection was flawed and in fact 30 people wanted this new type of bicycle. Now since the demand increased, according to the law of demand the price would also increase. Consequently, the rise in price will provide incentive for the company to produce more bicycles, thus increasing the supply. Next quarter, the company produces 20 more bicycles of this model. However, since 20 people already bought this type of bicycle only 10 more people would like to buy one. This will not cause the prices of the bicycles to increase. In fact, the price of the remaining bicycles will decrease since the demand is so low compared to the supply. Consequently more people will be able to afford this new type of bicycle.

The following picture illustrates the law of supply and demand:

The above picture shows the concept of supply and demand. You can see that when the price is low, the demand is higher than the quantity supplied, leading to shortage of the good. On the other hand, if the price is too high, the supply is higher than demand, hence we have a surplus of the good. Note that the intersection of the supply and demand curves is the market equilibrium point, which means that the optimal price for the item (so as to avoid shortage or surplus) is about 2.3 in this case. In theory, any supply-demand system should tend to the market equilibrium point.