Solve Econ Math Problem: Price & Quantity of Apples

[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: Q_D = 100 - 2P

Supply: Q_S = 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 Q_D = Q_S = 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.

Q_D = 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?

 

[airborne18]

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: Q_D = 100 - 2P

Supply: Q_S = 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 Q_D = Q_S = 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.

Q_D = 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.

 

[JThompson]

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