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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?
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:
Simplify both sides.
Subtract 50 from both sides.
Divide both sides by 10.
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) = $15 and Qs=Qd=75 units
I will start by writing in full some terms given in the question in short form.
DOL = dollar ($), 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.
Equilibrium price = 15 $, and equilibrium quantity = 75 units.
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