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The supply of an individual firm indicates the various quantities of a good (or service) a firm is willing and able to produce and supply to the market for sale at different possible prices, during a particular time period, ceteris paribus.

According to the law of supply, there is a positive causal relationship between the quantity of a good supplied over a particular time period and its price, ceteris paribus: as the price of the good increases, the quantity of the good supplied also increases; as the price falls, the quantity supplied also falls, ceteris paribus.

The reasoning offered for the law of supply makes sense to some extent, too: Higher prices generally mean that the firm’s profits increase, and so the firm faces an incentive to produce more output. Lower prices mean lower profitability, and the incentive facing the firm is to produce less. Therefore, there results a positive relationship between price and quantity supplied: the higher the price, the greater the quantity supplied.

However, to me, possibly due to the way the definition is phrased with “willing and able to produce to the market at different possible prices,” I feel that the negative relationship of demand would be the relationship for price and supply as well:

Here’s my reasoning: If I am a farmer, and some authoritative figure, such as the government, that is determined to plot graphs of the economy from real world data goes up to the only supplier of corn, me, and asks me for a set of prices, "how much would you be willing and able to produce and supply to the market", I would first determine how much income I would be at least satisfied with, almost determining a minimum wage for myself, and accordingly, I would divide this minimum wage by the set of prices the government wants to collect data on, to in effect end up on how much I’d be willing to produce and supply for each given price:

If I say that I’d be happy with 500 a week, and the government asks for data on the prices (10, 20, 30, 40, 50), because I would have to sell lesser units of corn for each higher price to achieve the 500 I have set as the minimum wage I’d have to receive to be willing and able to produce corn to the market, my units of corn at each price would be 50, 25, 17, 13, 10 respectively.

This way, supply would have a negative relationship with price…

To me, both reasonings make sense, however, I can’t say that the first one that explains the law of supply outweighs the reasoning I presented. What’s flawed in this reasoning?

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One flaw in your reasoning where you get a negative relationship between price and supply is to assume a monopolist. With a monopolist the "market supply curve" as such does not exist! The monopolist looks at the demand curve and chooses(!) his optimal point, he doesn't draw up a supply curve, since he has all the power.

Furthermore, since a monopolist chooses his optimal point on the demand curve, the monopolist's reasoning (as you describe) incorporates the demand curve, which is decreasing in prices. Hence you get that relation. Furthermore, since he incorporates the demand curve we can't speak of a supply curve (which must be independent of the demand curve to have sense) as such.

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The "flaw" in your reasoning is that you assume a firm wants to have a fixed amount of revenue, and then it will adjust its quantity produced as price changes, in order to always have this fixed amount of revenue (however the firm determines its magnitude). Then of course, as price goes up, the firm will produce less in order not to exceed the targeted level of revenues.

So what if you could earn "600 a week"? Would you say "no, I want to earn no more than 500"? Well, maybe you would say that, you and perhaps many other people -but the experience from actual markets is that most firms don't think that way. And in Economics, we do not model anything that can happen (and everything can happen when humans are involved); we try instead to model what usually, predominantly, happens.

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