It seems to me that the law of demand has to be wrong in some cases. There

Question:

It seems to me that the law of demand has to be wrong in some cases. There are plenty of examples of the price of a good rising and people buying more of the good. For example, during the period 2000–2006, house prices were rising (sometimes quite rapidly) in the United States and all you heard about back then was how house sales were up. In other words, prices were up and house sales were up. That seems to me to contradict the law of demand, which states that if prices rise, sales will go down.
Here what and how the economist thinks:
This person is making a very fundamental mistake. He thinks that the higher price is what causes people to buy more, when it is people who want to buy more that causes the higher price.

EXHIBIT 14

Think of a downward sloping demand curve, like the one shown in Exhibit 14(a). At a price of $$10,$ the quantity demanded is 100; and at the higher price of $$12,$ the quantity demanded is 80. This

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illustrates the law of demand: a higher price brings about a lower quantity demanded.
Now look at panel

(b) in Exhibit 14(b). When the demand curve is D1, and the equilibrium price is $$10,$ the quantity demanded is 100.
Now suppose demand rises, and the demand curve shifts rightward from D1 to D2 . First, what happens to the equilibrium price of the good?
It rises from $$10$ to $$12.$ Now ask yourself what the quantity demanded is at $$12,$ given that the demand curve has shifted rightward? The answer is that it is 120. In other words, we see that the quantity demanded is higher at $$12$ than it was at $$10—but$ this is because the demand curve shifted rightward, it is not because of the higher price alone.
Let’s now think about what was happening in the period 2000– 2006 when house prices were rising and house sales were rising too. Was it the higher house prices that caused the greater house sales? No. Instead, it was the increased demand for houses that caused both the higher house prices and the higher house sales.
Questions:
1. Suppose the equilibrium price of a good is currently $$4.$ Then something happens to cause it to rise to $$6.$ Under what condition will quantity demanded be higher at $$6$ than at $$4?$ Under what condition will quantity demanded be lower at $$6$ than at $$4?
2.$ The law of demand states that as the price of a good rises, quantity demanded falls; and as the price of a good falls, quantity demanded rises. Is it important to add that the law of demand holds when all other things are held constant or nothing else changes? Explain your answer in terms of the person who argued that house prices increased and house sales increased too.