SUPPLY, SUPPLY CURVE, SUPPLY SCHEDULE AND SUPPLY FUNCTION

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Supply refers to the number of goods and services that suppliers (sellers) are willing and able to sell at a given price. It is a fundamental economese.

What a seller receives for a unit of a product is called price. The unit of a product sold is called quantity supplied

Usually, a price increase will lead to an increase in the quantity supplied; a price decrease will lead to a decrease in the quantity supplied. 

This is such ubiquitous that it has now come to be called the law of supply. This law holds all other economic factors constant.

Just like demand, the relationship between price and quantity can be represented in a table or what economists called the supply schedule. Here is a presumed supply schedule of books

Price(€)
Quantity supplied(units)
10
1000
20
1600
30
2000
40
2400
50
2900
60
3500

The above can also be represented on a supply curve. A supply curve is a graphical representation of the price and quantity supplied pairings.

In other words, the supply curve is the graphical representation of the price and quantity pairings listed on the supply schedule. 

A typical supply curve is upward-sloping or positive-sloping, reflecting the positive relationship between price and quantity supplied. Below is an example of a supply curve. 

Notice that price is on the vertical axis while quantity is on the horizontal axis.



CHANGE IN QUANTITY SUPPLY VS CHANGE IN SUPPLY
In economics, a change in quantity supply is not the same as a change in supply. 

Change in quantity supply is usually influenced by a change in the good's price (all things being equal).

As you saw earlier, a change in quantity is represented as a movement along the supply curve.

Change in supply, On the other hand, is caused by economic factors (other than the good's price). 

But what are these non-price factors that cause a change in supply? how do they affect supply? These and more questions will be answered below.

Cost of production
This is probably the most vital factor that affects supply. 

The cost of input like land, labour, raw material invariably affects supply. 

To illustrate, when there is a rise in the price of input (say raw material), the supply curve will shift inward because few suppliers will sell at prevalent prices.

Why?
Higher costs reduce the supplier's profit margin. 

Conversely, a fall in the price of input will shift the supply curve outward because sellers are now willing to sell more goods. 

Why?
Lower costs mean a higher profit margin.

Technological improvement
When a seller discovers a new technology that enables him to produce at a lower cost, the supply curve will shift outward.

This is because the seller will be able to produce a greater quantity at a lower cost.

Government policy and regulation
Government regulations like taxes, subsidies also influence supply. 

When governments impose a tax on goods, the manufacturing company will be unwilling to produce the goods since taxes will increase their cost and reduce their profit margin. 

Subsidies have the opposite effect. Government subsidies (such as grants) will shift the supply curve outward as firms would produce more goods than they would have if there was no subsidy.

So, it is safe to say "more tax, less supply, more subsidy, more supply"

Weather and natural conditions
Natural conditions like weather, flooding could affect supply. Bad weather conditions will shift the supply curve inward; a Lot of flooding will affect seller (especially farmer) output. 

Conversely, Good weather will shift the supply curve outward.

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Supplier's expectation of future prices
Another factor that affects supply is price expectation. If suppliers expect the price to rise, they will hoard goods so that they could sell for a high price later. 

This action will lead to a decrease in supply.

Conversely, if suppliers expect the price to fall, they will increase supply now, to avoid selling at a much lower price.

When these five non-price factors influence supply, then it is called a shift in the supply curve/change in supply. The accompanying graph shows a shift in supply

When the supply curve shifts inward(from $S_2$ to $S_0$), it is called a decrease in supply. 

Conversely, an outward shift of the supply curve (from $S_0$ to $S_2$) is called an "increase in supply"

Having explained the factors that influence supply, we now turn our attention to the supply function. 

A supply function represents the supply of goods and services as a function of all factors that affect supply.
$Q_x^S$=f($P_x$, C, ....)
 Where $Q_x^S$ is the quantity supplied for good x
             $p_x$ is the price of good x
              C is the cost of production good x

Example
A firm weekly supply for pens is given by the supply function:

$Q_{pn}^s=-129+75P_{pn}+15C$
Where $Q_{pn}^s$ is the quantity of pens supplied
             $P_{pn}$ is the price of the pen
             C is the cost of producing a pen
Given that the price of the pen is €10, the Cost of production is €7
1. Determine the weekly supply of pens
2. Given the value of C, determine the inverse supply function.

Take note of the positive sign of the coefficient of $P_{pn}$. this indicates the positive relationship between price and quantity supplied.

1.) $Q_{pn}^s=-129+75P_{pn}+15C$
Insert the values of all variables
$Q_{pn}^s=-129+75(10)+15(7)$
$Q_{pn}^s=-129+750+105$
$Q_{pn}^s=726$

2) Before we find the inverse supply function, let's find the quantity and price relationship.
$Q_{pn}^s=-129+75P_{pn}+15(7)$
$Q_{pn}^s=-129+105+75P_{pn}$
$Q_{pn}^s=-129+105+75P_{pn}$
$Q_{pn}^s=-24+75P_{pn}$
The inverse supply function means the price should be expressed as a function of the quantity supplied. So we are just going to do simple maths
$Q_{pn}^s=-24+75P_{pn}$
$-75P_{pn}=-24-Q_{pn}^s$

Divide through by 75
$\frac{\require{cancel}\bcancel{-75}P_{pn}}{\require{cancel}\bcancel{-75}}=\frac{\require{cancel}\bcancel{-}24}{\require{cancel}\bcancel{-}75}-\frac{Q_{pn}^s}{-75}$
$P_{pn}=\frac{8}{25}-\frac{Q_{pn}^s}{-75}$.
$P_{pn}=\frac{8}{25}-\frac{(-Q_{pn}^s)}{75}$.
$P_{pn}=\frac{8}{25}+\frac{Q_{pn}^s}{75}$.

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