Sellers of goods are either individuals who has previously bought a good (which can be stored for a while) but now wants to sell it, instead of consuming it themselves, or producers that specialize in producing new items of the good. Since most such production takes place in organization called firms we will equalize producers with firms. Everyone knows that firms are “in it” for the profit (this is not always true, but we will let this pass...) and when they decide how much to produce at a given price they will do this with an eye on “the bottom line”, i.e., on the effect on the entire firm’s profit. If they can sell one better at a price that will exceed the extra cost it incurs by producing it, total profits are increased, and the firm will go ahead and supply the extra units on the market. It is therefore primarily the cost of production that affects a firm’s supply and its pursuit of profits.

Profits, by the way is the difference between the revenue it gets from the goods it sells and the cost of producing these goods. The cost of producing one more unit of a good depends on the cost of variable factors of production, i.e., everything needed in the production process to produce another quantity of the good. It may be an extra hour of labor, electricity, water and a myriad of other material inputs. If all these ingredients (or inputs) are bought at a fixed price, the price of inputs will affect supply. It is often assumed, even though it does not have to be the case, that it becomes more and more difficult to produce an extra unit of a good, the more that is already produced. More “difficult” we can equalize with more expensive, or costly. This leads to the conclusion that the supply curve usually slopes upwards. A firm that wants the highest profit possible will stop supplying at the point there the extra revenue it receives from selling another unit of the good is exactly equal to the additional costs it incurs; to supply more it has to be compensated by a higher price. The supply curve shows the relationship between the price of a good and the quantity supplied. If the price of one or more of the inputs needed in the production process changes, the entire supply curves shifts. We call such shifts a change in supply. So, remember that a movement along a supply curve is referred to as a change in quantity supplied and a shift of the entire curve is a change in supply.
A supply curve can be written in general as:

QS = b + βo.p + β + βl.w,

Where βo is the slope of the supply curve, or the marginal effect on the quantity supplied by a unit increase in the own price

ΔQS/Δp = βo,

pm is the price of some material input and w is the price of labor, βm and βl are the marginal effects of a unit change in these prices (on supply), i.e., these are shift factors. If the price of any input increases supply will decrease, or the entire supply curve will shift downwards, hence we expect βm and βl, to both be negative; βo if also often assumed to be positive.

As an example, consider the following supply function for a liter of beer:

QS = 27 + 3.p – − 0.05. w,

Where pm could be the price of malt, an important ingredient in making beer. If pm = 1kr and w = 100kr, we can write the supply curve as:

QS = 27 + 3xp – 2x1 − 0.05 x100
= 20 + 3p

To follow the convention of putting price on the vertical axis, we solve for the inverse supply curve as:

pS(Q) = (-20/3) + (1/3) Q.

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