Hi,
The demand for inflatable garden gnomes is given by P = 300 – 2Q, while the supply of is P= 100 + Q/2. How many garden gnomes are traded in equilibrium?
I found the answer to be Q = 80.
The related question was the one I had difficulty with:
Suppose that the market for gnomes is yet to reach equilibrium, and that the current price and quantity in the market for gnomes in the previous question is P = 150 and Q = 75. What is the absolute value of the elasticity of demand at this point on the demand curve? (Remember to rearrange the demand curve!)
The multiple choices given were 0.5, 0.25, 2, 4 or 1. However I seem to keep getting 0.875 using the price elasticity formula.
Thanks!
i'm doing the same question and i found it to be 1, however i did not rearrange the demand curve. how are we supposed to reaggrange the curve? confused *
To find the absolute value of the elasticity of demand at a specific point on the demand curve, you need to use the price elasticity of demand formula, which is:
Elasticity of Demand = (Percentage change in quantity demanded) / (Percentage change in price)
To calculate the percentage change in quantity demanded, you need to find the difference between the initial quantity demanded and the new quantity demanded, and then divide that difference by the initial quantity demanded.
Percentage change in quantity demanded = (New quantity demanded - Initial quantity demanded) / Initial quantity demanded
Similarly, to calculate the percentage change in price, you need to find the difference between the initial price and the new price, and then divide that difference by the initial price.
Percentage change in price = (New price - Initial price) / Initial price
In this case, the initial price is 150 and the new price is 100. So:
Percentage change in price = (100 - 150) / 150 = -0.3333
The initial quantity demanded is 75 and the new quantity demanded is 80. So:
Percentage change in quantity demanded = (80 - 75) / 75 = 0.0667
Now, you can plug these values into the formula to find the elasticity of demand:
Elasticity of Demand = (0.0667) / (-0.3333) = -0.2001
Since we are interested in the absolute value, the elasticity of demand at this point on the demand curve is 0.2001.