Solving for equilibrium price and quantity mathematically

Summary

This video tutorial guides viewers through the mathematical process of determining equilibrium price and quantity in microeconomics. It outlines four key steps: expressing demand and supply functions in terms of quantity, setting supply equal to demand to find the equilibrium point, solving for the equilibrium price, and verifying by calculating the equilibrium quantity. An example is used to illustrate these steps, showing how to manipulate equations to solve for 'q' and 'p', and ensuring accuracy by checking both the supply and demand functions.

Takeaways

• 📚 The video provides a step-by-step guide to finding equilibrium price and quantity in microeconomics.
• 🔢 The first step is to express the demand and supply functions in terms of quantity (Q) rather than price (P).
• ✏️ Example: Transforming the demand function from q_d = 10,000 - 80p to p = (10,000 - q_d) / 80.
• 🔄 The second step involves setting the quantity supplied equal to the quantity demanded to find the equilibrium point.
• 💡 Solving for equilibrium price (p) is the third step, which is done by equating the supply and demand equations and solving the resulting equation.
• 📉 The video explains that the equilibrium price is where the supply and demand curves intersect on a typical graph.
• 🔍 The fourth and final step is to plug the equilibrium price back into the supply and demand functions to find the equilibrium quantity.
• 🔗 It's important to verify the equilibrium quantity by checking it against both the supply and demand functions to ensure accuracy.
• 📈 The example given demonstrates how the law of demand (quantity demanded decreases as price increases) and the law of supply (quantity supplied increases as price increases) are reflected in the equations.
• 📝 The video script serves as a tutorial for students learning introductory microeconomics, emphasizing the importance of algebraic manipulation and graph interpretation.

Q & A

What is the main topic of the video?

The main topic of the video is how to find equilibrium price and quantity mathematically for an introductory microeconomics course.

How many steps are involved in finding equilibrium price and quantity according to the video?

There are four steps involved in finding equilibrium price and quantity as described in the video.

What is the first step in finding equilibrium price and quantity?

The first step is to solve the demand and supply functions in terms of quantity, meaning to express the functions with quantity (q) as the subject.

What does setting quantity of supply equal to quantity demanded represent?

Setting quantity of supply equal to quantity demanded represents the condition at the equilibrium point where the supply and demand curves intersect on a typical supply and demand graph.

How do you solve for the equilibrium price (p)?

To solve for the equilibrium price (p), you set the quantity supplied equal to the quantity demanded, then solve the resulting equation for p.

What is the purpose of plugging the equilibrium price back into the supply and demand functions?

Plugging the equilibrium price back into the supply and demand functions is done to solve for the equilibrium quantity and to check that the calculations are correct.

What is an example of a demand function given in the video?

An example of a demand function given in the video is qd = 10,000 - 80p, which is already solved for in terms of quantity (qd).

How does the video demonstrate converting a demand function into terms of quantity?

The video demonstrates converting a demand function into terms of quantity by manipulating the equation to isolate qd, and then solving for p to get the function in terms of q.

What is the example supply function given in the video?

The example supply function given in the video is 20p, which confirms the law of supply where quantity supplied increases as price increases.

How does the video ensure the accuracy of the calculated equilibrium price and quantity?

The video ensures the accuracy by plugging the calculated equilibrium price into both the supply and demand functions and verifying that the same equilibrium quantity is obtained.

What is the final equilibrium price and quantity found in the video example?

In the video example, the final equilibrium price is found to be $100, and the equilibrium quantity is 2,000 units.