# 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 UNITSWHAT IS THE EQULIBRIUM PRICE AND QUANTITY?

Asked on by jhghjhygt

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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?

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The equilibrium price is that price for which quantity of demamand is equal to the quantity of supply. The law of demand and supply given is:

Qs = 50, Qd=100 when price is \$10 and for every \$1 rise in price ,  Qs increases by 5 units and Qd decrases by 5 units.

If we say  that x dollar increase in price, then by the given law, the quantities of supply and demand are: Qs= 50+5*xand Qd= 100-5*x. Further we suppose that x dollar increase also results in equilibrium price, equilibrium quantity of supply and demand. Therefore, for equilibrium Qs=Qd or 50+5*x=100-5*x.Solve the equation for x as below:

Add 5x to both sides:

50+5x+5x=100-5x+5x.

Simplify both sides.

50+10x=100.

Subtract 50 from both sides.

50+10x-50=100-50

Simplify.

10x=50.

Divide both sides by 10.

10x/10=50/10.

x=5.

Therefore, if we increse the price by x = 5 dollars, the quantity of supply =50+5x=50+5*5=75 units and the quantity of demand = 100-5x=100-5*5=75. Therefore, the equilbrium price = \$(10+x) = \$(10+5) = \$15 and Qs=Qd=75 units

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

I will start by writing in full some terms given in the question in short form.

DOL = dollar (\$), QS = quantity offered for supply, and QD = quantity demanded.

Coming to the answers to the question, the table below gives the QS and QD at different prices.

Price in \$   QS      QD

10             50      100

11             55       95

12             60       90

13             65       85

14             70       80

15             75       75

16             80       70

17             85       65

From the above table we see that at price of 15 \$ both QS and QD are 75 units.

Therefore:

Equilibrium price = 15 \$, and equilibrium quantity = 75 units.

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