Why Supply and Demand Are Hard to Measure

Over at Economix, Catherine Rampell asks, “Does lowering the price of broadband increase its use?”
This provides a useful teaching moment. She collected data on broadband prices and adoption rates in different countries; and by linking lower prices with more broadband adoption, she’s trying to figure out the demand curve.
Unfortunately though, empirical economics isn’t that simple. Imagine instead that a supply-obsessed economist were interested in asking “Does increasing use of broadband raise its price?” Similar logic might lead him to examine data on broadband prices and adoption rates — yes, the same data — but he would expect to see more broadband correlated with higher prices because the supply curve is upward sloping.
So does a graph of broadband prices and quantities in different countries tell us about the supply curve or the demand curve? Unfortunately, it’s a mishmash. Let me explain. Prices and quantities are determined by both supply and demand. If both curves were the same in every country, broadband prices and use would be the same in every country. However that’s not what we observe. Prices and quantities differ across countries. But is this because their supply curves differ or their demand curves differ?
If the supply curve differs across countries — perhaps because it is more costly to lay cable in some places — then some countries will be on the leftmost part of the demand curve (high price, low quantity), and others will be on the rightmost part of the demand curve (low price, high quantity), with some in between. This is case 1 in my chart below; in this example, the cross-country data would be where the black crosses are. This must be what Rampell has in mind when she says “As Econ 101 would predict, the two measures are related: prices go down, subscription rates go up.”

But this isn’t all that Econ 101 suggests. What about case 2, where the demand curve varies across countries? People in rich countries like the U.S., Western Europe, and Scandinavia are probably willing to pay more for broadband access than people from Poland, Turkey, Mexico, or other poorer countries. My graph shows that poor countries will be on the leftmost part of the supply curve (low price and quantity), and rich countries will be on the right side (high price and quantity), with some in between. This is not just a story just about G.D.P. by the way — there are many other reasons demand may differ across countries. But whatever the reason, the black crosses representing the data would suggest that high prices are associated with high quantities, even though all demand curves are clearly downward-sloping.
So we have two cases, both of which have downward-sloping demand curves, but in one, the quantity of broadband subscribers is low in countries with high broadband prices; and in the alternative case, broadband subscriptions are high in countries with high broadband prices. In reality, the world is a mixture of both cases. The conclusion from this little example: when you plot real-world price and quantity data, you don’t learn the slope of the demand curve (unless you are strictly in case 1), and you don’t learn the slope of the supply curve (unless you are strictly in case 2). Instead you learn a combination of the slope of both demand and supply, and the extent to which variation is driven by these two forces.
The data that Rampell compiled are shown in the graph below. At first blush it looks like a mystery, as broadband price and quantity don’t look to be closely related, leading her to ask: “So what gives? Why isn’t there a stronger relationship between price and use?”
What gives is that the real world is serving up healthy doses of both case 1 and case 2: both supply and demand curves are different around the world. Consequently, we see low broadband prices yielding high adoption rates in case-1 countries (as Rampell expected) and low adoption rates in case-2 countries (check out all the poorer countries below her regression line, below). And the reverse pattern holds for high broadband prices. That is, you can’t infer supply or demand curves from simply looking at price and quantity data. For the technically minded, this is called the identification problem, and it is why econometrics is so darn difficult. This problem — the bane of most economists’ lives — arises precisely because prices and quantities are determined by both blades of the supply and demand scissors.
Armed with a little bit of economic theory, the poor fit between price and quantity isn’t such a mystery after all.