Price and Equilibrium Analysis

Welcome to Section 7. In this section, you will learn about the equilibrium situation in the market, which occurs when the quantity of goods or services supplied equals the amount demanded at a certain price. This is a key concept for understanding how markets in Ghana, such as the market for fish or tomatoes balance the supply and demand. When the market is in equilibrium, there is neither a surplus nor a shortage of goods, and businesses can operate smoothly. You will also discover how to determine the equilibrium price and quantity. By looking at where supply and demand curves intersect, you will learn how to calculate the price at which goods are sold and the quantity that buyers are willing to purchase at that price. This will help you understand how market forces like changes in consumer preferences or weather conditions can affect prices in real life.

KEY IDEAS

• At equilibrium, the price of a good or service is stable, as the forces of supply and demand are balanced, and neither buyers nor sellers have an incentive to change the price.

• The equilibrium situation in the market occurs when the quantity demanded by consumers equals the quantity supplied by producers, meaning there is no surplus or shortage of goods.

• The equilibrium quantity is the amount of goods that buyers are willing to purchase at the equilibrium price, and it is the same amount that producers are willing to supply.

• To determine the equilibrium price and quantity, you need to find the point where the supply and demand curves intersect, representing the price and quantity at which the market is balanced.

In Economics, market equilibrium is a condition or situation where the quantity of goods or services supplied is equal to the quantity of goods demanded. The equilibrium condition involves a stable market price for the goods and services consumed. It strikes a balance between the quantities or amount of goods or services demanded and the amount the amount or quantities of goods or services the producer is willing to put forward on the market.

1. Supply refers to the quantities or amount of goods or services that producers are willing and able to sell at various prices over a period of time.

2. Demand refers to the quantities of a good or service that consumers are willing and able to purchase at various prices over a period of time.

3. The equilibrium price is the price at which the quantity of a good supplied over some time equals the quantity of goods or services demanded.

4. The equilibrium quantity also is the number of goods and services bought and sold at the equilibrium price which is expressed mathematically as “market equilibrium is reached when the Quantity (Qd) equals the Quantity supplied (Qs).

Figure 7.1: A graphical illustration of a market equilibrium Demand Function The demand function is the mathematical expression that shows how price of a commodity varies with the quantity demanded of the commodity. This is expressed as the function:

Qd = a - bP Where: ‘Qd’ is the quantity demanded, ‘P’ is the price of the commodity, ‘b’ is the gradient or slope (which measures the variability of the price with the quantity), ‘a’ is the constant or the tendency for the consumer to consume more.

In this context, the demand function can also be referred to as the demand equation:

Qd=a−bP Supply Function The supply function is the mathematical expression that shows how the quantity supplied of a commodity varies with the price of the commodity.

This is expressed as the function Qs = c + dP Where: ‘Qs’ is the quantity supplied, ‘P’ is the price of the commodity, ‘d’ is the gradient or slope which measures how much the quantity supplied changes in response to a change in price, ‘c’ is a constant indicating the baseline quantity supplied when the price is zero; it reflects the producer’s tendency to supply a certain amount regardless of price.

In this context, the supply function can also be referred to as the supply equation Qs = c+ dP

Activity 7.1 Understanding Market Equilibrium

Instructions In this activity, you will learn about market equilibrium, where supply and demand meet, by using infographics and practicing graphing the concept.

1. What is Market Equilibrium?

2. Use paper or a digital tool like PowerPoint to draw line graphs of supply (slopes up from left to right) and demand (slopes down from left to right) curves showing the point where the two curves intersect. This is the equilibrium point.

3. Label the equilibrium price and the equilibrium quantity on the graph.

4. What happens at the equilibrium price, and how is the number of goods buyers want to purchase equal to the amount that sellers want to sell?

5. Write or make a short audio report on your findings.

6. Share your report with the class for discussion and feedback. Respect and accept others’ feedback and support your friends who are struggling.

In the market situation, the equilibrium price and the equilibrium quantity is derived by determined the equilibrium point. This is done by combining the two equations for the quantity demanded with the quantity supplied.

Follow the procedure below step by step:

Given:

• Demand Equation: Qd=a−bP

• Supply Equation: Qs=c+dP

Step 1: To find the equilibrium, set the demand function equal to the supply function:

Qd = Qs

Step 2: Substitute the given equations: a−bP = c+dP

Step 3: Solve the equation in step 2 to find P:

a. Rearrange the equation (change sides change sign): a−c = bP+dP

b. Combine the terms with P using factorisation: a−c = P(b+d)

c. Divide both sides of the equation by (b+d): P =

Step 4: Now you know equilibrium price P in terms of a, b, c and d this can be is substituted it back into either the demand or supply function to find the equilibrium quantity Q.

For example, the demand and supply function of pineapples is given as Qd = 100 - 2P and Qs = 20 + 3P. Calculate the equilibrium price.

Answer At equilibrium Qd = Qs, but Qd =100 - 2P and Qs = 20 + 3P Equating Qd to Qs gives 100 - 3P = 20 + 3P 100 - 20 = 3P + 2P (grouping like terms) 80 = 5P P = 16 The equilibrium price is 16 units.

To find the equilibrium quantity, you will substitute the value of the equilibrium price, P=16 for P in any of the equations. That is considering the demand function Qd=100- 2P and substituting the value of P into Qd =100 - 2P, gives Qd = 100 - 2(16) Qd =100 - 32 Qd =100 Substitute P=16 for P in Qs=20+3P Qs = 20+3(16) Qs = 20+48 Qs = 68 units Hence, at equilibrium Qd = Qs, ie 68 = 68.

Activity 7.2 Understanding Market Equilibrium Using Algebra

Instructions In this activity, you will explain market equilibrium with simple algebra. Imagine that the demand function and supply function for a product are given as:

Demand Function (Qd) = 50 - 2P and Supply Function (Qs) = 10 + 3P. where ‘P’ represents the price, and Qd and QS represent the quantity demanded and supplied respectively.

1. Write down the equilibrium function by equating the demand function to the supply function.

2. Calculate for P (price) when Qd = Qs by making price the subject of the equation.

3. Substitute the value of ‘P’ as derived in step 2 above into either the demand or supply function and solve carefully to arrive at the equilibrium quantity.

4. Draw the demand and supply curves on a graph. Label the axes (the vertical axis represents the price, and the horizontal axis represents the quantity).

5. Plot the equilibrium price (P = 8) and the equilibrium quantity (Q = 34) on the graph.

6. Mark the point where the supply and demand curves intersect. This is your market equilibrium.

7. What do the equilibrium price and equilibrium quantity you have calculated mean?

8. Make a short presentation on your findings using PowerPoint, audio, or written report.

9. Share your presentation with the class for discussion and feedback.