Taking into account the demand curve and the definition of price elasticity of demand:
a) the quantity demanded is 300 for the given price.
b) the price elasticity of demand if the price of good decreases from $100 to $90 is -0.5625.
Consider the demand curve for a good is given by: Demand=500−2×P and suppose that the good’s price is $100.
a) Considering that the demand curve represents all the quantities of a good or service that buyers would be willing and could buy at all possible prices, to calculate the quantity demanded for the given price you should replace the price P with $ 100:
Demand=500−2×$100
Solving:
Demand=500− 200
Demand= 300
Finally, the quantity demanded is 300 for the given price.
b) The price elasticity of demand indicates how much the quantity demanded of a good changes when its price changes. It is defined as the percentage change in quantity demanded divided by the percentage change in price.
Then the price elasticity of demand can be expressed as:
E= (ΔQ÷Q) ÷ (ΔP÷P)
In this case, you first calculate the change in the quantities.
To do this, the change in the quantities is obtained by subtracting from the final demand to the initial demand, the final quantity being 500- 2×90= 320 and the initial quantity 500 - 2×100= 300.
So the change in the quantities is: ΔQ= 320 - 300= 20
And the initial quantity Q= 320
On the other side, the price change is obtained by subtracting the final price from the initial price. This is ΔP= 90 - 100= -10
And the initial price P = 90
Replacing in the definition of price elasticity of demand:
E= (20÷320) ÷ [(-10)÷90]
Solving=
E= -0.5625
Finally, the price elasticity of demand if the price of good decreases from $100 to $90 is -0.5625.
Learn more about price elasticity of demand:
