Your firm sells product Gamma. The own price elasticity of Gamma is -0.5. The pr

Question

Your firm sells product Gamma. The own price elasticity of Gamma is -0.5. The price of Gamma is $20 and the quantity sold of Gamma is 100. Suppose the price of Gamma is raised to $30. What is the new quantity sold of Gamma? The answer is below, but I cannot figure out how he got 75.

Here:

E = -0.5

Q = X (to be determined)

Q = 100

P = $10 (i.e. $30-$20)

P = $20

OR -0.5 = (X/100) / (10/20)

OR X = -25 (solve for yourself)

Q = -25

OR (New quantity – Old quantity) = -25

OR (New quantity – 100) = -25

OR New quantity = 75 (solve for yourself)

If the price of Gamma is raised to $30, the new quantity sold of Gamma is 75.

Explanation / Answer

formula of price elasticity of demand

=change in quantity / change in price) *(price/quantity)

it tells you how quantity change with change in price

-0.5 = (x/10) * (20/100)

-0.5 = (x/10) *0.20

-0.5/0.2 = x/10

-2.5 = x/10

x=25 i.e change in quantity

earlier we have quantity of 100

new = 100-25 =75

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