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Demand and Supply Functions and Market Equilibrium Welcome visitors to the mathematic.my.id blog,,

In this post, we will explain about the function of supply and demand and market balance.


Demand Function

Demand function is a function that relates the number of products demanded by consumers with the price of goods in a certain period.

The general form of the demand function is:
$$P=a-bQ$$ or $$Q=a-bP$$ where:
$P$ = item price per unit.
$Q$ = quantity demanded.
$a$ = constant number.
$b$ = slope/gradient.

Supply Function

If we are a seller or trader, then when the price of goods rises, we will sell the goods entirely with the aim of getting maximum profit.

So we know that the relationship between prices and goods in a supply function is directly proportional.

Supply is the number of goods or services offered by producers to consumers in a certain period of time.

Here is the general form of the supply function:
$$P=a+bQ$$ or $$Q=a+bP$$ where:
$P$ = item price per unit.
$Q$ = quantity demanded.
$a$ = constant number.
$b$ = slope/gradient.


The formula for determining the demand and supply functions

The discussion of the supply and demand functions above is a general form that must be understood.
Consider the following formula:
$$\frac{P-P_1}{P_2-P_1}=\frac{Q-Q_1}{Q_2-Q_1}$$ where:
$P$ = price.
$P_1$ = first price.
$P_2$ = scond price.
$Q$ = number of demand/supply.
$Q_1$ = first number of demand/supply (in accordance with the $P_1$).
$Q_2$ = second number of demand/supply (in accordance with the $P_2$).

Example 1:
If the price of an item is 2 usd per unit, then the quantity demanded is 10 units. And if the price of goods is 1 usd per unit, then the number of requests is 20 units. Determine the equation of the demand function!
Solution:
Known:
$P_1=2,$ $\quad Q_1=10$
$P_2=1,$ $\quad Q_2=20$.
$$\frac{P-2}{1-2}=\frac{Q-10}{20-10}$$ $$\frac{P-2}{-1}=\frac{Q-10}{10}$$ $$P-2=1-\frac{1}{10}Q$$ $$P=3-\frac{1}{10}Q$$
Example 2:
When the price is 4 usd per unit, the quantity offered is 10 units. And when the price is 6 usd per unit, then the quantity offered is 20 units. Determine the supply function!
Solution:
Known:
$P_1=4$, $~Q_1=10$.
$P_2=6$, $~Q_2=20$.
$$\frac{P-4}{6-4}=\frac{Q-10}{20-10}$$ $$\frac{P-4}{2}=\frac{Q-10}{10}$$ $$P-4=\frac{1}{5}Q-2$$ $$P=2+\frac{1}{5}Q$$

Market Equilibrium

Market equilibrium is a condition in which there is a balance between the quantity of a product or service demanded and offered at a certain price.

The market equilibrium formula is as follows:
$$Q_d=Q_s$$ where:
$Q_d$: number of demand.
$Q_s$: number of supply.

Example:

It is known that the function of a demand for goods $Q_d = 40-P$ and the function of supply goods $Q_s= 4P-50$. What is the market equilibrium price and quantity?.


Solution: $$Q_d=Q_s$$ $$40-P=4P-50$$ $$-P-4P=-50-40$$ $$-5P=-90$$ $$P_E=18$$ So the market equilibrium price is $P_E=18$.

To find the market equilibrium quantity ($Q_E$) then substitute $P_E=P$ into $Q_d$ or $Q_s$. Suppose we substitute $P_E$ into $Q_d$ then we get: $Q_E=40-18=22$. So the total market equilibrium is 22.


Thus this post, see you in other posts and hopefully useful.