Monday, July 21, 2014

Supply and Demand

When many people think of 'economics,' the first idea that comes to mind is 'supply and demand.' Consumers of business news are quite used to commentators and analysts, when asked why gas prices have risen, or why wages are low, or why salmon costs more than tuna, explaining that 'It's supply and demand.'

What exactly does that mean? Most people probably have an intuitive sense; 'supply' refers in some way to the amount of something that is for sale, and 'demand' refers in some way to how much people want. This is basically right. But think about it: both of those intuitive definitions are referring only to quantities. So where do prices come in? To answer that question, we've got to think clearly about demanders and suppliers.

Demand for a good is not simply a number. After all, aren't you willing to buy more of something when it costs less, all else equal? In fact, we could plot the quantity of a good that you'd be willing and able to buy at each possible price. This is called a demand schedule. We could then connect all of these points, and we'd get a downward-sloping curve like the blue one in the example below. This is the demand curve. When we talk about demand broadly, we are referring to this curve, which shows the quantity demanded at different prices, all else equal.

A quick note here on Ceteris Paribus. This Latin phrase means "with other things the same," and it is a foundational concept in economic analysis. The most basic economic analysis involves observing a set of facts about prices, quantities sold, and other attributes of a market, and then changing one fact, such as the income level of the buyers of a good, and calculating the resultant change in the prices, quantities, etc.

So we've seen how a demand curve is derived; the supply curve is derived similarly. If someone owns something, they may be willing to sell it. The amount that a given person will sell is typically an increasing function of the market price of that item. Also, a rise in market price will draw into the market potential suppliers who were unwilling to supply any of the item at the lower price. Thus, the supply schedule is the quantity that people are willing and able to sell at a given price. As with demand, a curve that traces out the supply schedule is the supply curve, and it shows the quantity supplied at different prices, all else equal.

Now that we've defined and derived demand and supply, we can use them to determine the quantity traded in the marketplace, and the market price at which that trading happens. Price and quantity are jointly determined and, since we have two equations and two unknowns, we can solve this system of equations. A typical demand equation takes the form

Qd = a - b * P

where a is the intercept and b is the slope. The intercept can be thought of as the quantity that people would buy if the price were zero. (Economists like to display price on the y axis; it's a quirk of the discipline.) The slope is the reduction in quantity demanded induced by an incremental rise in price. (Again, this is a logical approximation, as the demand curve is generally treated as continuous. For simplifying purposes, we will also regard both demand and supply curves as linear, though this rarely holds empirically.) Similarly, a typical supply equation takes the form

Qs = c + d * P

where c is the intercept and d is the slope. In the case of supply, the slope is the additional incremental price rise required for suppliers to supply an additional incremental quantity. (The intercept is conceptually a bit more complicated in a supply equation.)

Since we know that quantity demanded must equal quantity supplied in equilibrium, one way to solve this simple system is to substitute thusly

a - b * P = c + d * P

and solve for P:

P = ( a - c ) / ( d + b )

We can then substitute this value of P into either the demand or the supply equation to solve for Q:

Q = a - b * ( a - c ) / ( d + b ) = c + d * ( a - c ) / ( d + b )

We can see from these solutions that interactions between (even simplified) demand and supply curves can be complex. Recall from above that the intercept for a demand equation contains all of the information about potential consumers other than their reaction to price changes. In other words, the slope of a demand curve represents the consumers' response to price changes, and other factors that may affect demand, such as the incomes and preferences of consumers, and the prices of other goods, affect the intercept. Therefore, if consumers suddenly prefer more of a good, say, lemons, at any given price (perhaps because they have learned that lemons prevent scurvy), then the intercept shifts to the right in a parallel manner. But if consumers prefer ten more lemons at any given price than previously, does that mean that ten more lemons will be sold? No! This is because, as we saw above, price and quantity are jointly determined by supply and demand.

We can show this in the interactive demonstration below. As the demand curve shifts out, the price rises as the equilibrium point moves along the supply curve. This causes the price to rise, which causes a shift back along the demand curve. Thus, an outward shift in demand causes a (smaller) rise in quantity and a rise in price. This holds for all markets with upward-sloping supply curves and downward-sloping demand curves (the most common situation). Similarly, an inward shift of the demand curve will cause a reduction in both quantity and price.

The supply curve can also shift in or out in a parallel manner. This would also be due to factors other than price. For example, people who make and sell handicrafts may develop more efficient ways to make their goods, allowing them to make them faster, and sell them for less. Alternately, the prices they pay for the raw materials they use could rise, forcing them to sell the same goods for a higher price. When supply shifts inward (selling less at a given price), price goes up, but quantity goes down. Similarly, when supply shifts outward (selling more at a given price), price goes down and quantity goes up.

The effects of changes in the responsiveness of demand and supply to price are a bit more complicated, but the demonstration below allows the user to observe these effects, as well as the effects of changes in the intercepts.

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