Price is 10 DOL, QS is 50 units, and the QD is 100 units. For every 1 DOL rise in price, QS rises by 5 units and QD falls by 5 units. What is the equilibrium price and quantity?

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The new equilibrium price will occur where the new supply and new demand are equal. First, we will determine the change in price needed to achieve equal supply and demand by setting up a simple algebraic equation based on the information given. We know that for every dollar rise in...

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The new equilibrium price will occur where the new supply and new demand are equal. First, we will determine the change in price needed to achieve equal supply and demand by setting up a simple algebraic equation based on the information given. We know that for every dollar rise in price, supply (currently 50) increases by 5 units (+5). We also know that for every dollar rise in price, demand (currently 100) decreases by 5 units (-5). Starting with the original information we create the equation:

1. QS +5P = QD - 5P

2. 50 + 5P = 100 - 5P

3. 10P = 50

4. P = 5

Now that we have the increase in price of $5 we can plug this information into the equation to determine equilibrium quantity for supply and demand:

1. 50 + 5P = 100 - 5P

2. 50 + 5*5 = 100 - 5*5

3. 50 + 25 = 100 - 25

4. 75 = 75

We now see that the equilibrium quantity is 75 units.

We now take the increase in price of (+$5) and add it to the original price to find the new equilibrium price.

$10 + $5 = $15

The new equilibrium quantity is 75 units and the equilibrium price is $15 per unit.

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To answer this mathematically, we can set up a simple algebraic equation. First, we need to find the equilibrium price—the price at which the adjusted supply and adjusted demand are equal. Since the current demand (100) decreases by 5 for every dollar increase in price and the current supply increases by 5 for every dollar increase in price (P), the equation looks like this:

  1. New Supply = New Demand
  2. 50 + 5P = 100 - 5P
  3. 10P = 50
  4. P = 5

The price will increase by $5.

Plugging that back into step 2 of the equations, we get the following:

  1. 50 + (5*5) = 100 - (5*5)
  2. 75 = 75

The equilibrium supply and demand totals 75 units. Of course, to find the final price, we need to do some simple addition:

  1. New Price = 10 + P = 10 + 5 = 15

Thus, market equilibrium is 75 units supplied at $15 per unit.

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The equilibrium price will be $15 and the equilibrium quantity will be 75.

You can see that this is correct by doing the math.  We start out at a price of $10 with QS at 50 and QD at 100.

You say that for every dollar the price goes up, QS goes up 5 units and QD down by 5 units.

So, you take the $5 increase in price (from $10 to $15) and multiply that by 5 units.  That tells you that the QS will go up 25 units and the QD will go down 25 units.

That means that the QS goes from 50 up to 75 and the QD goes down from 100 to 75.  When QS and QD are equal, you have your equilibrium.

Did you need to know how to state this algebraically?

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