# Solve Econ Math Problem: Price & Quantity of Apples

• Error Prone
This is because at a price of 10, the quantity demanded and supplied are equal, resulting in the equilibrium point. The confusion may have arisen because you were trying to find the price at which demand would equal zero, when you should have been looking for the quantity at which demand would equal zero. The graph will help illustrate this concept.
Error Prone
I'm probably making a really stupid error (I often make those in numerical contexts!), but I'm having a bit of trouble with an introductory economics assignment that involves a little elementary algebra.

BACKGROUND: We learned about the supply-demand equilibrium - a price at which the quantity supplied equals the quantity demanded.

QUESTION: Suppose the demand & supply for apples is given by:

Demand: QD = 100 - 2P

Supply: QS = 50 + 3P

a) Solve for the equilibrium price and quantity for apples.

MY SOLUTION:

Well, I made both equations equal & solved for the unknowns:

100 - 2P = 50 + 3P
50 = 5P
P = 10

Since 50 + 3(10) and 100 - 2(10) both equal 80, then QD = QS = 80

And it seems all nice & what not, but then the next sub-question asks:

"With price on the vertical axis & quantity of apples on the horizontal axis, graph the demand & supply curves & illustrate the equilibrium price and quantity".

So, to try finding some points on the curve I tried to find the price at which demand would equal zero.

QD = 0 = 100 - 2P
2P = 100
P = 50

BUT 50 IS A LOWER PRICE THEN 80! And I was taught that the demand of a good goes up as it's price goes down, so this makes no sense. At 50, their should be more demand that at 80, NOT LESS!

Am I confusing something here?

Error Prone said:
I'm probably making a really stupid error (I often make those in numerical contexts!), but I'm having a bit of trouble with an introductory economics assignment that involves a little elementary algebra.

BACKGROUND: We learned about the supply-demand equilibrium - a price at which the quantity supplied equals the quantity demanded.

QUESTION: Suppose the demand & supply for apples is given by:

Demand: QD = 100 - 2P

Supply: QS = 50 + 3P

a) Solve for the equilibrium price and quantity for apples.

MY SOLUTION:

Well, I made both equations equal & solved for the unknowns:

100 - 2P = 50 + 3P
50 = 5P
P = 10

Since 50 + 3(10) and 100 - 2(10) both equal 80, then QD = QS = 80

And it seems all nice & what not, but then the next sub-question asks:

"With price on the vertical axis & quantity of apples on the horizontal axis, graph the demand & supply curves & illustrate the equilibrium price and quantity".

So, to try finding some points on the curve I tried to find the price at which demand would equal zero.

QD = 0 = 100 - 2P
2P = 100
P = 50

BUT 50 IS A LOWER PRICE THEN 80! And I was taught that the demand of a good goes up as it's price goes down, so this makes no sense. At 50, their should be more demand that at 80, NOT LESS!

Am I confusing something here?

Plot it and label the plot and you will figure out your confusion.

With Economics curves use anything, but plot it. You don't need complex math software, even a graphing calculator. The plot will illustrate the concept.

Last edited:
According to your work, the quantity was 80, not the price. The price was 10.

## 1. How do you calculate the optimal price and quantity of apples?

To calculate the optimal price and quantity of apples, you need to use the demand and supply curves. The point where the demand and supply curves intersect is the equilibrium price and quantity, which is considered the optimal price and quantity.

## 2. How do changes in demand and supply affect the price and quantity of apples?

If there is an increase in demand for apples, the equilibrium price and quantity will also increase. On the other hand, if there is a decrease in demand, the equilibrium price and quantity will decrease. Similarly, if there is an increase in supply, the equilibrium price will decrease and the quantity will increase. A decrease in supply will lead to an increase in the equilibrium price and a decrease in quantity.

## 3. What is the role of elasticity in determining the price and quantity of apples?

Elasticity measures the responsiveness of quantity demanded to changes in price. If the demand for apples is elastic, a small change in price will lead to a larger change in the quantity demanded. In this case, changes in price will have a significant impact on the equilibrium price and quantity. On the other hand, if the demand for apples is inelastic, changes in price will have a minimal effect on the equilibrium price and quantity.

## 4. How do you interpret the slope of the demand and supply curves in relation to the price and quantity of apples?

The slope of the demand curve reflects the price elasticity of demand, while the slope of the supply curve reflects the price elasticity of supply. A steeper demand curve indicates a more inelastic demand, while a flatter demand curve indicates a more elastic demand. A steeper supply curve indicates a more inelastic supply, while a flatter supply curve indicates a more elastic supply.

## 5. How do external factors, such as government policies, affect the price and quantity of apples?

External factors, such as government policies, can have a significant impact on the price and quantity of apples. For example, if the government imposes a tax on apples, it will increase the cost of production and lead to a decrease in supply, resulting in a higher equilibrium price and lower quantity. Similarly, if the government provides subsidies for apple production, it will lower the cost of production and increase supply, resulting in a lower equilibrium price and higher quantity.

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