What is the equation for market equilibrium quantity?

  

Suppose the equation for the demand curve in a market is P=120-1/5*Qd , where Qd is the quantity demanded and P is the price, Also, suppose the equation for the supply curve in the same market is P=1/10*Qs, where Qs is the quantity supplied. What are the market equilibrium quantity and price?

Introduction:
Market equilibrium is the point where the quantity of goods or services demanded is equal to the quantity supplied. The equilibrium price is the price where the demand and supply curves intersect. In this context, we will discuss the market equilibrium quantity and price using the given demand and supply curves.

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Description:
The market demand curve is represented by P=120-1/5*Qd where P is the price and Qd is the quantity demanded. On the other hand, the supply curve in the market is given by P=1/10*Qs where P is the price, and Qs is the quantity supplied.

To find the market equilibrium quantity and price, we need to find the point where these two curves intersect. To do so, we equate the demand and supply functions, which gives us:

120 – 1/5 * Qd = 1/10 * Qs

Solving for Qd, we get:

Qd = 800 – 2Qs

Now that we know the quantity demanded, we can substitute the value of Qd in any of the two equations to find the equilibrium price. Let’s use the demand curve equation:

P = 120 – 1/5 * (800 – 2Qs)

Solving for P, we get:

P = 40 + 2/5 * Qs

Therefore, the market equilibrium price is $40, and the market equilibrium quantity is 600 units. At this price, the quantity demanded equals the quantity supplied, ensuring that the market is in a state of equilibrium.

Objectives: Students will be able to calculate the market equilibrium quantity and price using the demand and supply equations.

Learning Outcomes:
1. Students will learn how to determine the equilibrium quantity and price in a market.
2. Students will understand how changes in demand and supply affect the market equilibrium price and quantity.
3. Students will be able to interpret and solve problems related to demand and supply using mathematical equations.

Solution:
To determine the market equilibrium quantity and price, we need to set the demand and supply equations equal to each other.

Equating the demand and supply equations, we get:

P = 120 – 1/5Qd (Demand Equation)
P = 1/10Qs (Supply Equation)

120 – 1/5Qd = 1/10Qs

Multiplying both sides by 10, we get:

1200 – 2Qd = Qs

Substituting Qs with 120 – 1/5Qd (from the demand equation), we get:

1200 – 2Qd = 120 – 1/5Qd

Simplifying, we get:

1080 = 3/5Qd

Multiplying both sides by 5/3, we get:

Qd = 1800

Substituting Qd with 1800 in the demand equation, we get:

P = 120 – 1/5(1800) = $420

Therefore, the market equilibrium quantity is 1800 and the market equilibrium price is $420.

Heading: Conclusion

The market equilibrium price and quantity are determined by the intersection of the demand and supply curves. An understanding of the demand and supply equations and their relationship is important to calculate and analyze the market equilibrium. The knowledge of equilibrium price and quantity can be useful in policy-making decisions for the market.

Solution 1:

To determine the market equilibrium quantity and price, we need to set the demand and supply equations equal to each other and solve for Q.

120 – (1/5)Qd = (1/10)Qs

Multiplying both sides by 10, we get:

1200 – 2Qd = Qs

We can then substitute the supply equation (P = 1/10 Qs) into this equation to solve for Qd:

1200 – 2Qd = 10P

1200 – 2Qd = 10(120 – (1/5)Qd)

Simplifying this equation:

1200 – 2Qd = 1200 – 2/5 Qd

Multiplying both sides by 5:

600 – Qd = -2/5 Qd

Multiplying both sides by -1 and simplifying:

Qd = 375

We can use either the demand or supply equation to solve for the equilibrium price:

P = 120 – (1/5)Qd

P = 120 – (1/5)(375)

P = 60

Therefore, the market equilibrium quantity is 375 and the market equilibrium price is $60.

Solution 2:

We can also graph the demand and supply curves to find the market equilibrium quantity and price.

On a graph where price is on the y-axis and quantity is on the x-axis, the demand curve would have a negative slope and the supply curve would have a positive slope.

The point where the two curves intersect is the market equilibrium.

Using the demand and supply equations given:

P = 120 – (1/5)Qd

P = (1/10)Qs

We can plot the demand and supply curves on the graph.

The point of intersection (where Qd = Qs) is at Q = 375 and P = $60.

Therefore, the market equilibrium quantity is 375 and the market equilibrium price is $60.

Suggested Resources/Books:

1. “Microeconomics: Theory and Applications” by Edgar K. Browning and Mark A. Zupan
2. “Principles of Microeconomics” by N. Gregory Mankiw
3. “Managerial Economics” by Christopher R. Thomas and S. Charles Maurice
4. “Intermediate Microeconomics: A Modern Approach” by Hal R. Varian
5. “Microeconomics: Principles, Applications and Tools” by Arthur O’Sullivan

Market Equilibrium Quantity and Price:

In microeconomics, market equilibrium refers to the point where the quantity of a product that has been supplied matches the quantity that has been demanded by consumers. In this case, we have a market where the demand curve equation is P=120-1/5*Qd and the supply curve equation is P=1/10*Qs. To find the market equilibrium quantity and price, we need to set these two equations equal to each other and solve for Q:

120-1/5*Q = 1/10*Q

Multiplying both sides by 10, we get:

1200 – 2Q = Q

Adding 2Q to both sides, we get:

1200 = 3Q

Dividing both sides by 3, we get:

Q = 400

Now that we know the market equilibrium quantity is 400, we can find the price by substituting Q back into either the demand or supply curve equation:

P = 120 – 1/5 * 400 = 40

Therefore, the market equilibrium quantity is 400 and the market equilibrium price is 40.

Similar Asked Questions:

1. What is market equilibrium?
2. How do you find the equilibrium quantity and price in a market?
3. What factors influence market equilibrium?
4. What is the difference between a demand curve and a supply curve?
5. How do changes in demand or supply affect market equilibrium?Suppose the equation for the demand curve in a market is P=120-1/5*Qd , where Qd is the quantity demanded and P is the price, Also, suppose the equation for the supply curve in the same market is P=1/10*Qs, where Qs is the quantity supplied. What are the market equilibrium quantity and price?

Introduction:
Market equilibrium is the point where the quantity of goods or services demanded is equal to the quantity supplied. The equilibrium price is the price where the demand and supply curves intersect. In this context, we will discuss the market equilibrium quantity and price using the given demand and supply curves.

Description:
The market demand curve is represented by P=120-1/5*Qd where P is the price and Qd is the quantity demanded. On the other hand, the supply curve in the market is given by P=1/10*Qs where P is the price, and Qs is the quantity supplied.

To find the market equilibrium quantity and price, we need to find the point where these two curves intersect. To do so, we equate the demand and supply functions, which gives us:

120 – 1/5 * Qd = 1/10 * Qs

Solving for Qd, we get:

Qd = 800 – 2Qs

Now that we know the quantity demanded, we can substitute the value of Qd in any of the two equations to find the equilibrium price. Let’s use the demand curve equation:

P = 120 – 1/5 * (800 – 2Qs)

Solving for P, we get:

P = 40 + 2/5 * Qs

Therefore, the market equilibrium price is $40, and the market equilibrium quantity is 600 units. At this price, the quantity demanded equals the quantity supplied, ensuring that the market is in a state of equilibrium.

Objectives: Students will be able to calculate the market equilibrium quantity and price using the demand and supply equations.

Learning Outcomes:
1. Students will learn how to determine the equilibrium quantity and price in a market.
2. Students will understand how changes in demand and supply affect the market equilibrium price and quantity.
3. Students will be able to interpret and solve problems related to demand and supply using mathematical equations.

Solution:
To determine the market equilibrium quantity and price, we need to set the demand and supply equations equal to each other.

Equating the demand and supply equations, we get:

P = 120 – 1/5Qd (Demand Equation)
P = 1/10Qs (Supply Equation)

120 – 1/5Qd = 1/10Qs

Multiplying both sides by 10, we get:

1200 – 2Qd = Qs

Substituting Qs with 120 – 1/5Qd (from the demand equation), we get:

1200 – 2Qd = 120 – 1/5Qd

Simplifying, we get:

1080 = 3/5Qd

Multiplying both sides by 5/3, we get:

Qd = 1800

Substituting Qd with 1800 in the demand equation, we get:

P = 120 – 1/5(1800) = $420

Therefore, the market equilibrium quantity is 1800 and the market equilibrium price is $420.

Heading: Conclusion

The market equilibrium price and quantity are determined by the intersection of the demand and supply curves. An understanding of the demand and supply equations and their relationship is important to calculate and analyze the market equilibrium. The knowledge of equilibrium price and quantity can be useful in policy-making decisions for the market.

Solution 1:

To determine the market equilibrium quantity and price, we need to set the demand and supply equations equal to each other and solve for Q.

120 – (1/5)Qd = (1/10)Qs

Multiplying both sides by 10, we get:

1200 – 2Qd = Qs

We can then substitute the supply equation (P = 1/10 Qs) into this equation to solve for Qd:

1200 – 2Qd = 10P

1200 – 2Qd = 10(120 – (1/5)Qd)

Simplifying this equation:

1200 – 2Qd = 1200 – 2/5 Qd

Multiplying both sides by 5:

600 – Qd = -2/5 Qd

Multiplying both sides by -1 and simplifying:

Qd = 375

We can use either the demand or supply equation to solve for the equilibrium price:

P = 120 – (1/5)Qd

P = 120 – (1/5)(375)

P = 60

Therefore, the market equilibrium quantity is 375 and the market equilibrium price is $60.

Solution 2:

We can also graph the demand and supply curves to find the market equilibrium quantity and price.

On a graph where price is on the y-axis and quantity is on the x-axis, the demand curve would have a negative slope and the supply curve would have a positive slope.

The point where the two curves intersect is the market equilibrium.

Using the demand and supply equations given:

P = 120 – (1/5)Qd

P = (1/10)Qs

We can plot the demand and supply curves on the graph.

The point of intersection (where Qd = Qs) is at Q = 375 and P = $60.

Therefore, the market equilibrium quantity is 375 and the market equilibrium price is $60.

Suggested Resources/Books:

1. “Microeconomics: Theory and Applications” by Edgar K. Browning and Mark A. Zupan
2. “Principles of Microeconomics” by N. Gregory Mankiw
3. “Managerial Economics” by Christopher R. Thomas and S. Charles Maurice
4. “Intermediate Microeconomics: A Modern Approach” by Hal R. Varian
5. “Microeconomics: Principles, Applications and Tools” by Arthur O’Sullivan

Market Equilibrium Quantity and Price:

In microeconomics, market equilibrium refers to the point where the quantity of a product that has been supplied matches the quantity that has been demanded by consumers. In this case, we have a market where the demand curve equation is P=120-1/5*Qd and the supply curve equation is P=1/10*Qs. To find the market equilibrium quantity and price, we need to set these two equations equal to each other and solve for Q:

120-1/5*Q = 1/10*Q

Multiplying both sides by 10, we get:

1200 – 2Q = Q

Adding 2Q to both sides, we get:

1200 = 3Q

Dividing both sides by 3, we get:

Q = 400

Now that we know the market equilibrium quantity is 400, we can find the price by substituting Q back into either the demand or supply curve equation:

P = 120 – 1/5 * 400 = 40

Therefore, the market equilibrium quantity is 400 and the market equilibrium price is 40.

Similar Asked Questions:

1. What is market equilibrium?
2. How do you find the equilibrium quantity and price in a market?
3. What factors influence market equilibrium?
4. What is the difference between a demand curve and a supply curve?
5. How do changes in demand or supply affect market equilibrium?

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