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In many economic charts with demand and supply curve, people often say the demand curve goes down with more quantity. But I will give you a really practical example, why I think they are wrong.

Imagine one can of coke is 1\$ in the shop.

now if quantity is 2 it means I am willing to pay 2\$ for two cans.

3 for 3\$ 4 for 4\$

It means the curve will go up with the quantity.

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Price in the context of demand and supply analysis normally means price per unit. Suppose as you say the shop charges \$1 per can. At that price per can there will be a maximum number, say $N$, of cans you are willing to buy (within the relevant time period). The combination of price \$1 and quantity $N$ defines one point on your individual demand curve.

That single point cannot indicate whether the curve is upward or downward sloping. To determine the direction of slope would require knowledge of the maximum number of cans you would be willing to buy at different unit prices.

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What you wrote does not seem to be closely connected to what economists mean by a demand curve. The demand curve shows how much of the good consumers are willing (and able) to buy at a given price. It is customary to graph the inverse of this function, and this inverse demand $P(q)$ is indeed downward sloping. The main reason behind this is that marginal utility is typically decreasing.

Consider your coke example and suppose you are on the beach. For a first can of coke, you might be willing to pay, say, \$2 because you are thirsty. For the second can it is probably less, say, \$1 because you just had a can. For the third, it is even less. Even less for the next one and so on. The more you consume of a good the less you value one additional unit.

Another reason could be a substitution effect. That is, you buy more cans of coke when, all else equal, its price decreases because coke is now relatively cheaper than Sprite and Pepsi.

The demanded quantity also can go up because of an income effect. That is, you can afford more cans of coke when the price goes down.

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There are two things you are confusing here:

1.- The willingness to pay for something is completely independent of what the price in the store is. We think of the willingness to pay as something that buyers have regardless of prices. For example, maybe the price of sodas is only \$3 but my willingness to pay is \$10 on really hot days, while more like \$1 on a winter day. Clearly, I will not buy in the winter and definitely buy in the summer. How many will I buy? Well, we don't really have enough information. Maybe the second unit of soda on a summer day is only valuable \$2 to me (in which case I won't buy it), or maybe my willingness to pay is now \$5 (in which case I will buy it). What about the third can of soda in this scenario, we clearly need more information again, etc.

Notice that if the price of soda goes up to \$6, that will have no impact whatsoever on my willingness to pay. It will only have an impact on my decision of whether to buy or not, but not on my intrinsic willingness to pay.

2.- In the demand graph, we always plot price per unit, as explained by @Adam Bailey, so in your example, you have a single point (i.e. when the price is \$1 dollar), so you cannot really say if it's going up or down. Further, you are making something funky with quantities, because what we mean by quantity in the demand graph is "the maximum amount of sodas that will be bought at that price (per soda)". So if the quantity is 100 and the price is \$1.5 the total dollar amount will be \$150, but the price is still \$1.5.

In this last case, we say that "at a price of \$1.5, 100 units are demanded", and conversely you can say that "preferences of consumers are such that exactly 100 units are associated with a willingness to pay of at least \$1.5" (no-one uses the last one, but it may help you connect all the concepts).

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