Equilibrium Price and Quantity in a Competitive Market: A Comprehensive Guide

To find the equilibrium price and quantity in a competitive market, we need to set the quantity demanded Qd equal to the quantity supplied Qs. Given the equations:

Qd 200 - 5P

Qs -100 10P

Calculation Process

Step 1: Set Qd equal to Qs

200 - 5P -100 10P

Step 2: Solve for P (price)

Rearranging the equation:

200 100 10P 5P

300 15P

Divide both sides by 15:

P frac{300}{15} 20

Step 3: Substitute P back to find Q (quantity)

Now that we have the equilibrium price P 20 we can substitute it back into either the demand or supply equation to find the equilibrium quantity. Let’s use the demand equation:

Qd 200 - 5(20) 200 - 100 100

Summary of Results

Equilibrium Price P: 20 currency units

Equilibrium Quantity Q: 100 units

Understanding the Equilibrium Price

The term equilibrium price refers to the price at which the quantity demanded by consumers equals the quantity supplied by producers. At this price, there is no tendency for the price to change as the market is in balance.

If the price were above the equilibrium, there would be a surplus (more supply than demand), leading to downward pressure on the price. If the price were below the equilibrium, there would be a shortage (more demand than supply), causing prices to rise.

Thus, the equilibrium price reflects a stable market condition where supply and demand are perfectly matched.

Equilibrium in Competitive Markets

To compute the equilibrium price and quantity, we can use the relation between Quantity Demanded (Qd) and Quantity Supplied (Qs) at the equilibrium level:

Qd Qs

Putting the linear functions provided:

200 - 5P -100 10P

300 15P

P frac{300}{15} 20

Thus, the equilibrium price is 20 currency units.

For determining the equilibrium quantity, we can substitute the value of P into any of the equations:

Qd 200 - 5P 200 - 5(20) 200 - 100 100 units

Qs -100 10P -100 10(20) -100 200 100 units

Since Qd and Qs would be the same at the equilibrium level, you can calculate using any of the equations and verify your answer by calculating both.

Why it is Called Equilibrium Price

The term equilibrium price indicates that at this price, the demand and supply of the goods are the same. For any price higher or lower than the equilibrium price, the market will be at unrest, and the forces will adjust accordingly to get back to equilibrium.

If the price is higher than the equilibrium price, suppliers would be willing to supply more quantity according to the Law of Supply. However, consumers would be willing to purchase less of the same commodity due to the Law of Demand, thus driving the price down till it reaches the equilibrium price. Conversely, if the price is lower than the equilibrium price, the demand would exceed the supply, leading to a shortage. This shortage would cause prices to rise until equilibrium is restored.